Author: "Takéo Takahashi" / Language: english - Searchworks@Jio Institute Digital Library Search Results

Your search keyword '"Takéo Takahashi"' showing total 72 results

Start Over Author "Takéo Takahashi" Language english

72 results on '"Takéo Takahashi"'

1. FLATNESS APPROACH FOR THE BOUNDARY CONTROLLABILITY OF A SYSTEM OF HEAT EQUATIONS.

Author: COLLE, BLAISE, LOHÉAC, JÉRÔME, and TAKÉO TAKAHASHI
Subjects: HEATING, DIFFUSION coefficients, HEAT equation, CARLEMAN theorem
Abstract: We study the boundary controllability of 2×2 system of heat equations by using a flatness approach. According to the relation between the diffusion coefficients of the heat equation, it is known that the system can be neither null-controllable nor null-controllable for any T>T0, where T0∈[0,∞]. Here we recover this result in the case that T0∈[0,∞) by using the flatness method, and we obtain an explicit formula for the control and for the corresponding solutions. In particular, the state and the control have Gevrey regularity in time and in space. [ABSTRACT FROM AUTHOR]
Published: 2024
Full Text: View/download PDF

2. Gevrey regularity for a system coupling the Navier-Stokes system with a beam : the non-flat case

Author: Mehdi Badra, Takéo Takahashi, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)
Subjects: Physics::Fluid Dynamics, Navier-Stokes system, Mathematics - Analysis of PDEs, Algebra and Number Theory, Gevrey class semigroups, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Geometry and Topology, 2010 Mathematics Subject Classification : 76D03, 76D05, 35Q74, 76D27, Analysis, Analysis of PDEs (math.AP), fluid-structure
Abstract: International audience; We consider a bi-dimensional viscous incompressible fluid in interaction with a beam located at its boundary. We show the existence of strong solutions for this fluid-structure interaction system, extending a previous result [3] where we supposed that the initial deformation of the beam was small. The main point of the proof consists in the study of the linearized system and in particular in proving that the corresponding semigroup is of Gevrey class.
Published: 2022
Full Text: View/download PDF

3. Existence and uniqueness of strong solutions for the system of interaction between a compressible Navier-Stokes-Fourier fluid and a damped plate equation

Author: Takéo Takahashi, Debayan Maity, Center for Applicable Mathematics [Bangalore] (TIFR-CAM), Tata Institute for Fundamental Research (TIFR), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Debayan Maity was partially supported by INSPIRE faculty fellowship (IFA18-MA128) and by Department of Atomic Energy, Government of India, under project no. 12-R & D-TFR-5.01-0520. Takéo Takahashi was partially supported by the ANR research project IFSMACS (ANR-15-CE40-0010)., and ANR-15-CE40-0010,IFSMACS,Interaction Fluide-Structure : Modélisation, analyse, contrôle et simulation(2015)
Subjects: Change of variables, fluid-structure interaction, R-sectorial operators, Fixed point, 01 natural sciences, Physics::Fluid Dynamics, Mathematics - Analysis of PDEs, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Uniqueness, 0101 mathematics, Physics, Small data, Applied Mathematics, Operator (physics), 010102 general mathematics, Mathematical analysis, Linear system, maximal regularity, General Engineering, General Medicine, compressible NavierStokesFourier system, 010101 applied mathematics, Computational Mathematics, Compressibility, strong solutions, General Economics, Econometrics and Finance, Displacement (fluid), Analysis, Analysis of PDEs (math.AP)
Abstract: The article is devoted to the mathematical analysis of a fluid–structure interaction system where the fluid is compressible and heat conducting and where the structure is deformable and located on a part of the boundary of the fluid domain. The fluid motion is modeled by the compressible Navier–Stokes–Fourier system and the structure displacement is described by a structurally damped plate equation. Our main results are the existence of strong solutions in an L p − L q setting for small time or for small data. Through a change of variables and a fixed point argument, the proof of the main results is mainly based on the maximal regularity property of the corresponding linear systems. For small time existence, this property is obtained by decoupling the linear system into several standard linear systems whereas for global existence and for small data, the maximal regularity property is proved by showing that the corresponding linear coupled fluid–structure operator is R -sectorial.
Published: 2021
Full Text: View/download PDF

4. Remark on the global null controllability for a viscous Burgers-particle system with particle supported control

Author: Arnab Roy, Mythily Ramaswamy, Takéo Takahashi, Chennai Mathematical Institute [Inde], Institute of Mathematics of the Czech Academy of Science (IM / CAS), Czech Academy of Sciences [Prague] (CAS), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Arnab Roy and Takéo Takahashi were partially supported by the ANR research project IFSMACS (ANR-15-CE40-0010). The three authors were partially supported by the IFCAM project 'Analysis, Control and Homogenization of Complex Systems'., and ANR-15-CE40-0010,IFSMACS,Interaction Fluide-Structure : Modélisation, analyse, contrôle et simulation(2015)
Subjects: 0209 industrial biotechnology, Work (thermodynamics), Point particle, 02 engineering and technology, 01 natural sciences, Physics::Fluid Dynamics, Mathematics - Analysis of PDEs, 020901 industrial engineering & automation, Position (vector), Fluid-structure interaction, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Mathematics - Optimization and Control, Mathematics, Particle system, Applied Mathematics, 010102 general mathematics, Null (mathematics), Mathematical analysis, AMS subject classifications. 35Q35, 35D30, 35D35, 35R37, 35L10, 93D15, 93D20, global controllability, Burgers' equation, Controllability, viscous Burgers equation, Optimization and Control (math.OC), Particle, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Analysis of PDEs (math.AP)
Abstract: International audience; This paper is devoted to study the controllability of a one-dimensional fluid-particle interaction model where the fluid follows the viscous Burgers equation and the point mass obeys Newton's second law. We prove the null controllability for the velocity of the fluid and the particle and an approximate controllability for the position of the particle with a control variable acting only on the particle. One of the novelties of our work is the fact that we achieve this controllability result in a uniform time for all initial data and without any smallness assumptions on the initial data.
Published: 2020
Full Text: View/download PDF

5. Controllability of a fuid-structure interaction system coupling the Navier--Stokes system and a damped beam equation.

Author: Buffe, Rémi and Takéo Takahashi
Subjects: *CONTROLLABILITY in systems engineering, *FLUID-structure interaction, *HEAT equation, *NONLINEAR systems, *EQUATIONS
Abstract: We show the local null-controllability of a fluid-structure interaction system coupling a viscous incompressible fluid with a damped beam located on a part of its boundary. The controls act on arbitrary small parts of the fluid domain and of the beam domain. In order to show the result, we first use a change of variables and a linearization to reduce the problem to the null-controllability of a Stokes-beam system in a cylindrical domain. We obtain this property by combining Carleman inequalities for the heat equation, for the damped beam equation and for the Laplace equation with high-frequency estimates. Then, the result on the nonlinear system is obtained by a fixed-point argument. [ABSTRACT FROM AUTHOR]
Published: 2023
Full Text: View/download PDF

6. SWITCHING CONTROLS FOR PARABOLIC SYSTEMS.

Author: Badra, Mehdi and Takéo Takahashi
Subjects: HEAT equation, CARLEMAN theorem
Abstract: We consider the controllability of an abstract parabolic system by using switching controls. More precisely, we show that, under general hypotheses, if a parabolic system is null-controllable for any positive time with N controls, then it is also null-controllable with the property that at each time, only one of these controls is active. The main difference with previous results in the literature is that we can handle the case where the main operator of the system is not self-adjoint. We give several examples to illustrate our result: coupled heat equations with terms of orders 0 and 1, the Oseen system or the Boussinesq system. [ABSTRACT FROM AUTHOR]
Published: 2023

7. Controllability to trajectories of a Ladyzhenskaya model for a viscous incompressible fluid

Author: Takéo Takahashi, Sergio Guerrero, Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), and ANR-20-CE40-0009,TRECOS,Nouvelles directions en contrôle et stabilisation: Contraintes et termes non-locaux(2020)
Subjects: General Mathematics, 010102 general mathematics, Mathematics::Analysis of PDEs, controllability to trajectories, 2010 Mathematics Subject Classification : 76D05, 93C20, 93B05, 93B07, Mechanics, Viscous incompressible fluid, Carleman estimates, 01 natural sciences, nonlocal spatial terms, Controllability, Physics::Fluid Dynamics, viscous incompressible fluid, 0103 physical sciences, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 010307 mathematical physics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Mathematics
Abstract: International audience; We consider the controllability of a viscous incompressible fluid modeled by the Navier-Stokes systemwith a nonlinear viscosity. To prove the controllability to trajectories, we linearize around a trajectory andthe corresponding linear system includes a nonlocal spatial term. Our main result is a Carleman estimatefor the adjoint of this linear system. This estimate yields in a standard way the null controllability of thelinear system and the local controllability to trajectories. Our method to obtain the Carleman estimate iscompletely general and can be adapted to other parabolic systems when a Carleman estimate is available.
Published: 2021

8. Existence of contacts for the motion of a rigid body into a viscous incompressible fluid with the Tresca boundary conditions

Author: Matthieu Hillairet, Takéo Takahashi, Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), and Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Physics, Gravity (chemistry), Cauchy stress tensor, General Mathematics, 2010 Mathematics Subject Classification : 74F10, 35R35, 35Q30, 76D05, 010102 general mathematics, Boundary (topology), Newton's laws of motion, Mechanics, Slip (materials science), Rigid body, 01 natural sciences, Domain (mathematical analysis), fluid-structure, 010101 applied mathematics, Physics::Fluid Dynamics, Navier-Stokes system, Mathematics - Analysis of PDEs, Tresca's boundary conditions, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Boundary value problem, 0101 mathematics, Analysis of PDEs (math.AP)
Abstract: International audience; We consider a fluid-structure interaction system composed by a rigid ball immersed into a viscous in-compressible fluid. The motion of the structure satisfies the Newton laws and the fluid equations are the standard Navier-Stokes system. At the boundary of the fluid domain, we use the Tresca boundary conditions, that permit the fluid to slip tangentially on the boundary under some conditions on the stress tensor. More precisely, there is a threshold determining if the fluid can slip or not and there is a friction force acting on the part where the fluid can slip. Our main result is the existence of contact in finite time between the ball and the exterior boundary of the fluid for this system in the bidimensional case and in presence of gravity.
Published: 2021
Full Text: View/download PDF

9. Approximate controllability and stabilizability of a linearized system for the interaction between a viscoelastic fluid and a rigid body

Author: Arnab Roy, Takéo Takahashi, Debanjana Mitra, Department of Mathematics, Indian Institute of Technology Bombay, Powai, Maharashtra 400076, India, Institute of Mathematics of the Czech Academy of Science (IM / CAS), Czech Academy of Sciences [Prague] (CAS), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
Subjects: 0209 industrial biotechnology, Control and Optimization, Structure (category theory), 02 engineering and technology, 93D15, 01 natural sciences, controllability, Domain (mathematical analysis), Viscoelasticity, finite dimensional controls 2010 Mathematics Subject Classification 76A10, 020901 industrial engineering & automation, Position (vector), 0101 mathematics, [MATH]Mathematics [math], Mathematics, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Order (ring theory), stabilizability, Rigid body, Exponential function, viscoelastic fluids, Controllability, 74F10, Control and Systems Engineering, Fluid-structure interaction systems, 93B52, Signal Processing, 35Q35
Abstract: International audience; We study control properties of a linearized fluid-structure interaction system, where the structure is a rigid body and where the fluid is a viscoelastic material. We establish the approximate controllability and the exponential stabilizability for the velocities of the fluid and of the rigid body and for the position of the rigid body. In order to prove this, we prove a general result for this kind of systems that generalizes in particular the case without structure. The exponential stabilization of the system is obtained with a finite-dimensional feedback control acting only on the momentum equation on a subset of the fluid domain and up to some rate that depends on the coefficients of the system. We also show that, as in the case without structure, the system is not exactly null-controllable in finite time.
Published: 2020

10. Feedback stabilization of parabolic systems with input delay

Author: Imene Aicha Djebour, Takéo Takahashi, Julie Valein, Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), The two first authors were partially supported by the ANR research project IFSMACS (ANR-15-CE40-0010). The third author was partially supported by the ANR research projects ISDEEC (ANR-16-CE40-0013) and ANR ODISSE (ANR-19-CE48-0004-01)., ANR-15-CE40-0010,IFSMACS,Interaction Fluide-Structure : Modélisation, analyse, contrôle et simulation(2015), ANR-16-CE40-0013,ISDEEC,Interactions entre Systèmes Dynamiques, Equations d'Evolution et Contrôle(2016), and ANR-19-CE48-0004,ODISSE,Synthèse d'observateur pour des systèmes de dimension infinie(2019)
Subjects: 0209 industrial biotechnology, Work (thermodynamics), Control and Optimization, Feedback control, parabolic systems, 2010 Mathematics Subject Classification 93B52, 93D15, 35Q30, 76D05, 93C20, 02 engineering and technology, 01 natural sciences, Navier-Stokes system, 020901 industrial engineering & automation, Mathematics - Analysis of PDEs, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Mathematics - Optimization and Control, Mathematics, delay control, Applied Mathematics, 010102 general mathematics, Mathematical analysis, stabilizability, finite-dimensional control, Nonlinear system, Transformation (function), Optimization and Control (math.OC), [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Constant (mathematics), Stationary state, Analysis of PDEs (math.AP)
Abstract: This work is devoted to the stabilization of parabolic systems with a finite-dimensional control subjected to a constant delay. Our main result shows that the Fattorini-Hautus criterion yields the existence of such a feedback control, as in the case of stabilization without delay. The proof consists in splitting the system into a finite dimensional unstable part and a stable infinite-dimensional part and to apply the Artstein transformation on the finite-dimensional system to remove the delay in the control. Using our abstract result, we can prove new results for the stabilization of parabolic systems with constant delay: the \begin{document}$ N $\end{document}-dimensional linear reaction-convection-diffusion equation with \begin{document}$ N\geq 1 $\end{document} and the Oseen system. We end the article by showing that this theory can be used to stabilize nonlinear parabolic systems with input delay by proving the local feedback distributed stabilization of the Navier-Stokes system around a stationary state.
Published: 2020
Full Text: View/download PDF

11. Local null controllability of a rigid body moving into a Boussinesq flow

Author: Takéo Takahashi, Arnab Roy, Center for Applicable Mathematics [Bangalore] (TIFR-CAM), Tata Institute of Fundamental Research [Bombay] (TIFR), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), ANR-15-CE40-0010,IFSMACS,Interaction Fluide-Structure : Modélisation, analyse, contrôle et simulation(2015), and Tata Institute for Fundamental Research (TIFR)
Subjects: Controllability, 0209 industrial biotechnology, Control and Optimization, Carleman inequality, Newton's laws of motion, 02 engineering and technology, system, 01 natural sciences, Physics::Fluid Dynamics, Rigid body, 020901 industrial engineering & automation, Position (vector), Fluid–structure interaction, Fluid-structure interaction, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Boussinesq, 0101 mathematics, Navier–Stokes equations, Physics, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Null (mathematics), Flow (mathematics), AMS subject classifications 35Q30, 93C20, 76D05, 93B05, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Navier-Stokes equations
Abstract: International audience; In this paper, we study the controllability of a fluid-structure interaction system. We consider a viscous and incompressible fluid modeled by the Boussinesq system and the structure is a rigid body with arbitrary shape which satisfies Newton's laws of motion. We assume that the motion of this system is bidimensional in space. We prove the local null controllability for the velocity and temperature of the fluid and for the position and velocity of rigid body for a control acting only on the temperature equation on a fixed subset of the fluid domain.
Published: 2019
Full Text: View/download PDF

12. Mathematical analysis of the motion of a rigid body in a compressible Navier-Stokes-Fourier fluid

Author: Debayan Maity, Marius Tucsnak, Takéo Takahashi, Bernhard H. Haak, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), ANR-15-CE40-0010,IFSMACS,Interaction Fluide-Structure : Modélisation, analyse, contrôle et simulation(2015), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)
Subjects: General Mathematics, Motion (geometry), R-sectorial operators, 76N10, strong, 01 natural sciences, AMS subject classifications 35Q30, symbols.namesake, Mathematics - Analysis of PDEs, Thermal insulation, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Boundary value problem, 0101 mathematics, solutions, Mathematics, fluid-particle interaction, Small data, business.industry, 010102 general mathematics, Mathematical analysis, Linear system, maximal regularity, Rigid body, 76D05, 010101 applied mathematics, Fourier transform, Compressible Navier-Stokes-Fourier System, symbols, Compressibility, business, Analysis of PDEs (math.AP)
Abstract: International audience; We study an initial and boundary value problem modelling the motion of a rigid body in a heat conducting gas. The solid is supposed to be a perfect thermal insulator. The gas is described by the compressible Navier-Stokes-Fourier equations, whereas the motion of the solid is governed by Newton's laws. The main results assert the existence of strong solutions, in an L p-L q setting, both locally in time and globally in time for small data. The proof is essentially using the maximal regularity property of associated linear systems. This property is checked by proving the R-sectoriality of the corresponding operators, which in turn is obtained by a perturbation method.
Published: 2019
Full Text: View/download PDF

13. Gevrey regularity for a system coupling the Navier-Stokes system with a beam equation

Author: Takéo Takahashi, Mehdi Badra, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)
Subjects: Coupling, Gevrey class semigroups, Semigroup, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Boundary (topology), Fixed point, 01 natural sciences, Domain (mathematical analysis), fluid-structure, 010101 applied mathematics, Physics::Fluid Dynamics, Navier-Stokes system, Computational Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Uniqueness, 0101 mathematics, Gevrey class, 2010 Mathematics Subject Classification : 76D03, 76D05, 35Q74, 76D27, Analysis, Beam (structure), Mathematics
Abstract: International audience; We analyse a bi-dimensional fluid-structure interaction system composed by a viscous incompressible fluid and a beam located at the boundary of the fluid domain. Our main result is the existence and uniqueness of strong solutions for the corresponding coupled system. The proof is based on a the study of the linearized system and a fixed point procedure. In particular, we show that the linearized system can be written with a Gevrey class semigroup. The main novelty with respect to previous results is that we do not consider any approximation in the beam equation.
Published: 2019
Full Text: View/download PDF

14. Analysis of a simplified model of rigid structure floating in a viscous fluid

Author: Takéo Takahashi, Jorge San Martín, Marius Tucsnak, Debayan Maity, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Centre de modélisation mathématique (CMM), Universitad de Chile-Centre National de la Recherche Scientifique (CNRS), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), ANR-16-CE92-0028,INFIDHEM,Systèmes interconnectés de dimension infinie pour les milieux hétérogènes(2016), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Function space, Differential equation, Applied Mathematics, Mathematical analysis, return to equilibrium, General Engineering, Viscous shallow water equations, fluid-structure interaction, floating structure, Viscous liquid, 01 natural sciences, 010305 fluids & plasmas, 010101 applied mathematics, Viscosity, AMS subject classifications 35Q35 74F10, Flow (mathematics), Linearization, Modeling and Simulation, 0103 physical sciences, Fluid–structure interaction, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], strong solutions, 0101 mathematics, Shallow water equations, Mathematics
Abstract: International audience; We study the interaction of surface water waves with a floating solid constraint to move only in the vertical direction. The first novelty we bring in is that we propose a new model for this interaction, taking into consideration the viscosity of the fluid. This is done supposing that the flow obeys a shallow water regime (modeled by the viscous Saint-Venant equations in one space dimension) and using a Hamiltonian formalism. Another contribution of this work is establishing the well-posedness of the obtained PDEs/ODEs system in function spaces similar to the standard ones for strong solutions of viscous shallow water equations. Our well-posedness results are local in time for every initial data and global in time if the initial data are close (in appropriate norms) to an equilibrium state. Moreover, we show that the linearization of our system around an equilibrium state can be described, at least for some initial data, by an integro-fractional differential equation related to the classical Cummins equation and which reduces to the Cummins equation when the viscosity vanishes and the fluid is supposed to fill the whole space. Finally, we describe some numerical tests, performed on the original nonlinear system, which illustrate the return to equilibrium and the influence of the viscosity coefficient.
Published: 2019
Full Text: View/download PDF

15. Existence of weak solutions for a Bingham fluid-rigid body system

Author: Benjamin Obando, Takéo Takahashi, Departamento de Ingeniería Matemática [Santiago] (DIM), Universidad de Chile = University of Chile [Santiago] (UCHILE)-Centre National de la Recherche Scientifique (CNRS), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Centre National de la Recherche Scientifique (CNRS)-Universidad de Chile = University of Chile [Santiago] (UCHILE)
Subjects: Physics, Viscoplasticity, Applied Mathematics, Weak solution, 010102 general mathematics, Mathematical analysis, Newton's laws of motion, Weak formulation, Rigid body, 01 natural sciences, Displacement (vector), 010101 applied mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Penalty method, 0101 mathematics, Bingham plastic, Mathematical Physics, Analysis
Abstract: International audience; We consider the motion of a rigid body in a viscoplastic material. This material is modeled by the 3D Bingham equations, and the Newton laws govern the displacement of the rigid body. Our main result is the existence of a weak solution for the corresponding system. The weak formulation is an inequality (due to the plasticity of the fluid), and it involves a free boundary (due to the motion of the rigid body). We approximate it by regularizing the convex terms in the Bingham fluid and by using a penalty method to take into account the presence of the rigid body.
Published: 2019
Full Text: View/download PDF

16. Who should receive single-fraction palliative radiotherapy for gastric cancer bleeding?: An exploratory analysis of a multicenter prospective observational study (JROSG 17-3)

Author: Shuhei Sekii, Tetsuo Saito, Takashi Kosugi, Naoki Nakamura, Hitoshi Wada, Ayako Tonari, Hirofumi Ogawa, Norio Mitsuhashi, Kazunari Yamada, Takeo Takahashi, Kei Ito, Terufumi Kawamoto, Norio Araki, Miwako Nozaki, Joichi Heianna, Kenta Murotani, Yasuhiro Hirano, Atai Satoh, Tsuyoshi Onoe, and Naoto Shikama
Subjects: Gastric cancer, Radiotherapy, Palliative treatment, Medical physics. Medical radiology. Nuclear medicine, R895-920, Neoplasms. Tumors. Oncology. Including cancer and carcinogens, RC254-282
Abstract: Purpose: Although the Palliative Prognostic Index (PPI) has been used to predict survival in various cancers, to our knowledge, no study has examined its applicability in gastric cancer. This study aimed to determine the baseline PPI cutoff value for recommending single-fraction radiotherapy in patients with bleeding gastric cancer. Materials and methods: This was a secondary analysis of the Japanese Radiation Oncology Study Group (JROSG) 17–3, a multicenter prospective study of palliative radiotherapy for bleeding gastric cancer. Discrimination was evaluated using a time-dependent receiver operating characteristic curve, and the optimal cutoff value was determined using the Youden index. A calibration plot was used to assess the agreement between predicted and observed survival. Results: We enrolled 55 patients in JROSG 17–3. The respective median survival times were 6.7, 2.8, and 1.0 months (p = 0.021) for patients with baseline PPI scores of ≤ 2, 2 4. The areas under the curve for predicting death within 2, 3, 4, and 5 months were 0.813, 0.787, 0.775, and 0.721, respectively. The negative predictive value was highest when survival
Published: 2023
Full Text: View/download PDF

17. Boundary local null-controllability of the Kuramoto-Sivashinsky equation

Author: Takéo Takahashi, Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), and ANR-15-CE40-0010,IFSMACS,Interaction Fluide-Structure : Modélisation, analyse, contrôle et simulation(2015)
Subjects: 0209 industrial biotechnology, Control and Optimization, Boundary (topology), 02 engineering and technology, 01 natural sciences, 020901 industrial engineering & automation, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Nonlinear Sciences::Pattern Formation and Solitons, Mathematics, Physics::Computational Physics, Kuramoto-Sivashinsky equation, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Null (mathematics), null controllability 2010 Mathematics Subject Classification: 93B05, Kuramoto–Sivashinsky equation, Controllability, Nonlinear system, Control and Systems Engineering, Signal Processing, 35K55, 93C10, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Beam (structure)
Abstract: International audience; We prove that the Kuramoto-Sivashinsky equation is locally controllable in 1D and in 2D with one boundary control. Our method consists in combining several general results in order to reduce the null-controllability of this nonlinear parabolic equation to the exact controllability of a linear beam or plate system. This improves known results on the controllability of Kuramoto-Sivashinsky equation and gives a general strategy to handle the null-controllability of nonlinear parabolic systems.
Published: 2017
Full Text: View/download PDF

18. On the reconstruction of obstacles and of rigid bodies immersed in a viscous incompressible fluid

Author: Erica L. Schwindt, Takéo Takahashi, Jorge San Martín, Departamento de Ingeniería Matemática [Santiago] (DIM), Centre National de la Recherche Scientifique (CNRS)-Universidad de Chile = University of Chile [Santiago] (UCHILE), Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO), Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Universidad de Chile = University of Chile [Santiago] (UCHILE)-Centre National de la Recherche Scientifique (CNRS), and Université d'Orléans (UO)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Convex hull, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Mathematics::Analysis of PDEs, Boundary (topology), Inverse problem, Rigid body, 01 natural sciences, 010101 applied mathematics, Physics::Fluid Dynamics, Nonlinear system, Classical mechanics, complex geometrical solutions, Geometrical inverse problems, fluid-structure interaction, Navier–Stokes system, enclosure method, Obstacle, Fluid–structure interaction, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Point (geometry), 0101 mathematics, Mathematics
Abstract: We consider the geometrical inverse problem consisting in recovering an unknown obstacle in a viscous incompressible fluid by measurements of the Cauchy force on the exterior boundary. We deal with the case where the fluid equations are the nonstationary Stokes system and using the enclosure method, we can recover the convex hull of the obstacle and the distance from a point to the obstacle. With the same method, we can obtain the same result in the case of a linear fluid-structure system composed by a rigid body and a viscous incompressible fluid. We also tackle the corresponding nonlinear systems: the Navier–Stokes system and a fluid-structure system with free boundary. Using complex spherical waves, we obtain some partial information on the distance from a point to the obstacle.
Published: 2017
Full Text: View/download PDF

19. A boundary control problem for the steady self-propelled motion of a rigid body in a Navier-Stokes fluid

Author: Ana L. Silvestre, Toshiaki Hishida, Takéo Takahashi, Nagoya University, Center for Computacional and Stochastic Mathematics (CEMAT), Instituto Superior Técnico, Universidade Técnica de Lisboa (IST), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), and ANR-15-CE40-0010,IFSMACS,Interaction Fluide-Structure : Modélisation, analyse, contrôle et simulation(2015)
Subjects: Boundary (topology), Motion (geometry), 01 natural sciences, Rotating body, Physics::Fluid Dynamics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Self-propelled motion, Navier stokes, 0101 mathematics, Mathematical Physics, Mathematics, 3-D Navier–Stokes equations, Steady state, Boundary control, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Rigid body, Asymptotic behavior, 010101 applied mathematics, Distribution (mathematics), Classical mechanics, Flow velocity, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Exterior domain, Analysis
Abstract: International audience; We study the self-propelled motions of a rigid body immersed in a viscous incompressible fluid which fills the exterior domain of the rigid body.The mechanism used by the body to reach the desired motion is modeled through a distribution of velocities at its boundary. The fluid motion is modeled by the stationary Navier-Stokes system. These equations are coupled with two relations for the balance of forces and torques.We prove that there exists a control allowing the rigid body to move with a prescribed rigid velocity provided the velocity is small enough. We also show that since the net force exerted by the fluid to the rigid body vanishes, we have a better summability of the fluid velocity than the classical summability result for the solutions of the stationary Navier-Stokes system in exterior domains.
Published: 2017
Full Text: View/download PDF

20. Feedback boundary stabilization of 2d fluid-structure interaction systems

Author: Mehdi Badra, Takéo Takahashi, Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), and ANR-15-CE40-0010,IFSMACS,Interaction Fluide-Structure : Modélisation, analyse, contrôle et simulation(2015)
Subjects: Applied Mathematics, 010102 general mathematics, Mathematical analysis, Boundary (topology), fluid-structure interaction, feedback stabilization, 01 natural sciences, Domain (mathematical analysis), 010101 applied mathematics, Physics::Fluid Dynamics, Nonlinear system, Classical mechanics, Position (vector), Fluid–structure interaction, No-slip condition, beam equation, Discrete Mathematics and Combinatorics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Navier-Stokes equations, Navier–Stokes equations, Analysis, Stationary state, Mathematics
Abstract: International audience; We study the feedback stabilization of a system composed by an incompressible viscous fluid and a deformable structure located at the boundary of the fluid domain. We stabilize the position and the velocity of the structure and the velocity of the fluid around a stationary state by means of a Dirichlet control, localized on the exterior boundary of the fluid domain and with values in a finite dimensional space. Our result concerns weak solutions for initial data close to the stationary state. Our method is based on general arguments for stabilization of nonlinear parabolic systems combined with a change of variables to handle the fact that the fluid domain of the stationary state and of the stabilized solution are different. We prove that for initial data close to the stationary state, we can stabilize the position and the velocity of the deformable structure and the velocity of the fluid.
Published: 2017
Full Text: View/download PDF

21. On the Navier–Stokes system with the Coulomb friction law boundary condition

Author: Takéo Takahashi, Jorge San Martín, Loredana Bălilescu, Departamento de Matemática = Mathematics Department [Florianópolis] (MTM), Centro de Ciências Físicas e Matemáticas [Florianópolis] (CFM), Universidade Federal de Santa Catarina = Federal University of Santa Catarina [Florianópolis] (UFSC)-Universidade Federal de Santa Catarina = Federal University of Santa Catarina [Florianópolis] (UFSC), Department of Mathematics [Pitesti], Faculty of Mathematics, Universitatea din Pitesti [Roumanie] (UPIT)-Universitatea din Pitesti [Roumanie] (UPIT), Center for Mathematical Modeling (CMM), Universidad de Chile = University of Chile [Santiago] (UCHILE), Departamento de Ingeniería Matemática [Santiago] (DIM), Centre National de la Recherche Scientifique (CNRS)-Universidad de Chile = University of Chile [Santiago] (UCHILE), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), ANR-15-CE40-0010,IFSMACS,Interaction Fluide-Structure : Modélisation, analyse, contrôle et simulation(2015), and Universidad de Chile = University of Chile [Santiago] (UCHILE)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Cauchy stress tensor, Applied Mathematics, General Mathematics, Weak solution, 010102 general mathematics, Mathematical analysis, General Physics and Astronomy, 010103 numerical & computational mathematics, Mixed boundary condition, 16. Peace & justice, 01 natural sciences, Coulomb's law, Physics::Fluid Dynamics, symbols.namesake, Classical mechanics, Law, symbols, No-slip condition, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Cauchy boundary condition, Uniqueness, Boundary value problem, 0101 mathematics, Mathematics
Abstract: International audience; We propose a new model for the motion of a viscous incompressible fluid. More precisely, we consider the Navier–Stokes system with a boundary condition governed by the Coulomb friction law. With this boundary condition, the fluid can slip on the boundary if the tangential component of the stress tensor is too large. We prove the existence and uniqueness of weak solution in the two–dimensional problem and the existence of at least one solution in the three–dimensional case, together with regularity properties and an energy estimate. We also propose a fully discrete scheme of our problem using the characteristic method and we present numerical simulations in two physical examples.
Published: 2017
Full Text: View/download PDF

22. Fluid-rigid structure interaction system with Coulomb's law

Author: Takéo Takahashi, Loredana Bălilescu, Jorge San Martín, Department of Mathematics [Pitesti], Faculty of Mathematics, Universitatea din Pitesti [Roumanie] (UPIT)-Universitatea din Pitesti [Roumanie] (UPIT), Departamento de Matemática = Mathematics Department [Florianópolis] (MTM), Centro de Ciências Físicas e Matemáticas [Florianópolis] (CFM), Universidade Federal de Santa Catarina = Federal University of Santa Catarina [Florianópolis] (UFSC)-Universidade Federal de Santa Catarina = Federal University of Santa Catarina [Florianópolis] (UFSC), Center for Mathematical Modeling (CMM), Universidad de Chile = University of Chile [Santiago] (UCHILE), Departamento de Ingeniería Matemática [Santiago] (DIM), Universidad de Chile = University of Chile [Santiago] (UCHILE)-Centre National de la Recherche Scientifique (CNRS), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), ANR-15-CE40-0010,IFSMACS,Interaction Fluide-Structure : Modélisation, analyse, contrôle et simulation(2015), and Centre National de la Recherche Scientifique (CNRS)-Universidad de Chile = University of Chile [Santiago] (UCHILE)
Subjects: Coulomb's law 2010 Mathematics Subject Classification: 35Q30, 01 natural sciences, Coulomb's law, Physics::Fluid Dynamics, Navier-Stokes system, symbols.namesake, 76D03, Neumann boundary condition, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Fluid-structure system, Boundary value problem, 0101 mathematics, Physics, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Mixed boundary condition, 16. Peace & justice, Robin boundary condition, 76D27, 010101 applied mathematics, Computational Mathematics, Classical mechanics, Dirichlet boundary condition, No-slip condition, symbols, Cauchy boundary condition, Cauchy theory, Analysis
Abstract: International audience; We propose a new model in a fluid-structure system composed by a rigid body and a viscous incompress-ible fluid using a boundary condition based on Coulomb's law. This boundary condition allows the fluid to slip on the boundary if the tangential component of the stress is too large. In the opposite case, we recover the standard Dirichlet boundary condition. The governing equations are the Navier-Stokes system for the fluid and the Newton laws for the body. The corresponding coupled system can be written as a variational inequality. We prove that there exists a weak solution of this system.
Published: 2017
Full Text: View/download PDF

23. Income and Employment of Patients at the Start of and During Follow-up After Palliative Radiation Therapy for Bone Metastasis

Author: Hiroki Shirato, MD, Hideyuki Harada, MD, Yukako Iwasaki, MS, Akifumi Notsu, PhD, Kazunari Yamada, MD, Haruka Uezono, MD, Yutaro Koide, MD, Hitoshi Wada, MD, Hikaru Kubota, MD, Naoto Shikama, MD, Takuya Yamazaki, MD, Kei Ito, MD, Joichi Heianna, MD, Yukinori Okada, MD, Ayako Tonari, MD, Shigeo Takahashi, MD, Takashi Kosugi, MD, Yasuo Ejima, MD, Norio Katoh, MD, Kayo Yoshida, MD, Takafumi Komiyama, MD, Nobue Uchida, MD, Misako Miwa, MD, Miho Watanabe, MD, Hisayasu Nagakura, MD, Tetsuo Saito, MD, Hiroko Ikeda, MD, Isao Asakawa, MD, Tateishi Seiichiro, MD, Takeo Takahashi, MD, and Naoyuki Shigematsu, MD
Subjects: Medical physics. Medical radiology. Nuclear medicine, R895-920, Neoplasms. Tumors. Oncology. Including cancer and carcinogens, RC254-282
Abstract: Purpose: The aim of this study was to understand the income and employment status of patients at the start of and during follow-up after palliative radiation therapy for bone metastasis. Methods and Materials: From December 2020 to March 2021, a prospective multi-institutional observational study was conducted to investigate income and employment of patients at the start of administration of radiation therapy for bone metastasis and at 2 and 6 months after treatment. Of 333 patients referred to radiation therapy for bone metastasis, 101 were not registered, mainly because of their poor general condition, and another 8 were excluded from the follow-up analysis owing to ineligibility. Results: In 224 patients analyzed, 108 had retired for reasons unrelated to cancer, 43 had retired for reasons related to cancer, 31 were taking leave, and 2 had lost their jobs at the time of registration. The number of patients who were in the working group was 40 (30 with no change in income and 10 with decreased income) at registration, 35 at 2 months, and 24 at 6 months. Younger patients (P = 0), patients with better performance status (P = 0), patients who were ambulatory (P = .008), and patients with lower scores on a numerical rating scale of pain (P = 0) were significantly more likely to be in the working group at registration. There were 9 patients who experienced improvements in their working status or income at least once in the follow-up after radiation therapy. Conclusions: The majority of patients with bone metastasis were not working at the start of or after radiation therapy, but the number of patients who were working was not negligible. Radiation oncologists should be aware of the working status of patients and provide appropriate support for each patient. The benefit of radiation therapy to support patients continuing their work and returning to work should be investigated further in prospective studies.
Published: 2023
Full Text: View/download PDF

24. GEVREY REGULARITY FOR A SYSTEM COUPLING THE NAVIER STOKES SYSTEM WITH A BEAM EQUATION.

Author: BADRA, MEHDI and TAKÉO TAKAHASHI
Subjects: *NAVIER-Stokes equations, *GEVREY class, *FLUID-structure interaction, *EQUATIONS
Abstract: We analyze a bidimensional fluid-structure interaction system composed of a viscous incompressible fluid and a beam located at the boundary of the fluid domain. Our main result is the existence and uniqueness of strong solutions for the corresponding coupled system. The proof is based on a the study of the linearized system and a fixed point procedure. In particular, we show that the linearized system can be written with a Gevrey class semigroup. The main novelty with respect to previous results is that we do not consider any approximation in the beam equation. [ABSTRACT FROM AUTHOR]
Published: 2019
Full Text: View/download PDF

25. Evaluation of robustness in hybrid intensity-modulated radiation therapy plans generated by commercial software for automated breast planning

Author: Norifumi Mizuno, Ryouhei Yamauchi, Jiro Kawamori, Tomoko Itazawa, Munefumi Shimbo, Keiichiro Nishimura, Takafumi Yamano, Shogo Hatanaka, Masatsugu Hariu, and Takeo Takahashi
Subjects: Medicine, Science
Abstract: Abstract This study aimed to evaluate the robustness against geometric uncertainties in the hybrid intensity-modulated radiation therapy (IMRT) plans generated by commercially available software for automated breast planning (ABP). The ABP plans were compared with commonly used forward-planned field-in-field (FIF) technique plans. The planning computed tomography datasets of 20 patients who received left-sided breast-conserving surgery were used for both the ABP and FIF plans. Geometric uncertainties were simulated by shifting beam isocenters by 2, 3, 5, and 10 mm in the six directions: anterior/posterior, left/right, and superior/inferior. A total of 500 plans (20 patients and 25 scenarios, including the original plan) were created for each of the ABP and FIF plans. The homogeneity index of the target volume in the ABP plans was significantly better (p
Published: 2022
Full Text: View/download PDF

26. Well-posedness for a one-dimensional fluid-particle interaction model

Author: Frédéric Lagoutière, Takéo Takahashi, Boris Andreianov, Nicolas Seguin, Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB), Université de Bourgogne (UB)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques d'Orsay (LM-Orsay), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Numerical Analysis, Geophysics and Ecology (ANGE), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), ANR-11-JS01-0006,CoToCoLa,Thématiques actuelles en lois de conservation(2011), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Seguin, Nicolas, and Jeunes Chercheuses et Jeunes Chercheurs - Thématiques actuelles en lois de conservation - - CoToCoLa2011 - ANR-11-JS01-0006 - JCJC - VALID
Subjects: Conservation law, Differential equation, Point particle, Applied Mathematics, Mathematical analysis, Ode, 35L65, 35L81, 35R06, 65M12, Fixed point, Non-conservative coupling, Burgers' equation, Burgers equation, Computational Mathematics, Splitting, Well-posedness, Wave-front tracking, Fixed-Point, Bounded variation, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Entropy (arrow of time), BV estimates, Analysis, Fluid-particle interaction, Mathematics
Abstract: The fluid-particle interaction model introduced by the three last authors in [J. Differential Equations, 245 (2008), pp. 3503-3544] is the object of our study. This system consists of the Burgers equation with a singular source term (term that models the interaction via a drag force with a moving point particle) and of an ODE for the particle path. The notion of entropy solution for the singular Burgers equation is inspired by the theory of conservation laws with discontinuous flux developed by the first author, Kenneth Hvistendahl Karlsen and Nils Henrik Risebro in [Arch. Ration. Mech. Anal., 201 (2011), pp. 26-86]. In this paper, we prove well-posedness and justify an approximation strategy for the particle-in-Burgers system in the case of initial data of bounded variation. Existence result for L∞ data is also given.
Published: 2014

27. Feedback stabilization of a simplified 1d fluid- particle system

Author: Mehdi Badra, Takéo Takahashi, Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est
Subjects: Change of variables, Feedback stabilization, Applied Mathematics, Mathematical analysis, Boundary (topology), Vis cous Burgers equation, 74F10, 35Q35, 76D55, 93C20, 93D15, Burgers' equation, Nonlinear system, Control theory, Fluid–structure interaction, Fluid-structure interaction, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Burgers vortex, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Exponential decay, Mathematical Physics, Analysis, Stationary state, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract: We consider the feedback stabilization of a simplified 1d model for a fluid–structure interaction system. The fluid equation is the viscous Burgers equation whereas the motion of the particle is given by the Newton's laws. We stabilize this system around a stationary state by using feedbacks located at the exterior boundary of the fluid domain. With one input, we obtain a local stabilizability of the system with an exponential decay rate of order σ σ 0 . An arbitrary order for the exponential decay rate can be proved if a unique continuation result holds true or if two inputs are used to stabilize the system. Our method is based on general arguments for stabilization of nonlinear parabolic systems combined with a change of variables to handle the fact that the fluid domains of the stationary state and of the stabilized solution are different.
Published: 2014
Full Text: View/download PDF

28. Existence of global weak solutions for a phase-field model of a vesicle moving into a viscous incompressible fluid

Author: Takéo Takahashi, Yuning Liu, Universität Regensburg (UR), Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), CORIDA, ANR-09-BLAN-0213,CISIFS,Controle et Identification pour les Systemes d'Interaction Fluide-Structure(2009), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, and Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM)
Subjects: Field (physics), General Mathematics, Navier-Stokes, Monotonic function, 01 natural sciences, Quantitative Biology::Subcellular Processes, Physics::Fluid Dynamics, Phase (matter), [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Membrane vesicle, 0101 mathematics, Physics, Physics::Biological Physics, phase-field, Vesicle, 010102 general mathematics, General Engineering, Mechanics, Viscous incompressible fluid, vesicle membrane, 010101 applied mathematics, Compact space, Classical mechanics, local incompressibility, fluid vesicle interaction, Convection–diffusion equation
Abstract: International audience; We consider in this article a model of vesicle moving into a viscous incompressible fluid. The vesicle is described through a phase-field equation and through a transport equation modeling the local incompressibility of its membrane. The equations for the fluid are the classical Navier--Stokes equations with a force resulting from the presence of the vesicle. The model for the system vesicle--fluid is an approximation of a model obtained by Jamet and Misbah. Our main result states the existence of weak solutions for the corresponding system. The proof is based on compactness/monotonicity arguments
Published: 2014
Full Text: View/download PDF

29. On the identifiability of a rigid body moving in a stationary viscous fluid

Author: Takéo Takahashi, Carlos Conca, Erica L. Schwindt, Departamento de Ingeniería Matemática [Santiago] (DIM), Universidad de Chile = University of Chile [Santiago] (UCHILE)-Centre National de la Recherche Scientifique (CNRS), Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Universidad de Chile = University of Chile [Santiago] (UCHILE)
Subjects: Physics, Applied Mathematics, MSC: 49K40, 65J22, 76D05, 010102 general mathematics, Boundary (topology), Fluid mechanics, Herschel–Bulkley fluid, Mechanics, Viscous liquid, Rigid body, 01 natural sciences, Computer Science Applications, Theoretical Computer Science, 010101 applied mathematics, Physics::Fluid Dynamics, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Signal Processing, Compressibility, Identifiability, Convex body, 0101 mathematics, Mathematical Physics
Abstract: International audience; This paper is devoted to a geometrical inverse problem associated with a fluid-structure system. More precisely, we consider the interaction between a moving rigid body and a viscous and incompressible fluid. Assuming a low Reynolds regime, the inertial forces can be neglected and, therefore, the fluid motion is modelled by the Stokes system. We first prove the well posedness of the corresponding system. Then we show an identifiability result: with one measure of the Cauchy forces of the fluid on one given part of the boundary and at some positive time, the shape of a convex body and its initial position are identified.
Published: 2012
Full Text: View/download PDF

30. Existence of strong solutions for the motion of an elastic structure in an incompressible viscous fluid

Author: Takéo Takahashi, Muriel Boulakia, Erica L. Schwindt, Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Numerical simulation of biological flows (REO), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centro de Modelamiento Matemático [Santiago] (CMM), Centre National de la Recherche Scientifique (CNRS)-Universidad de Santiago de Chile [Santiago] (USACH), Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria), Universidad de Santiago de Chile [Santiago] (USACH)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), and Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)
Subjects: existence and uniqueness of strong solutions, Applied Mathematics, deformable structure, 010102 general mathematics, Mathematical analysis, Linear elasticity, MSC: 74F10, 76D03, 35Q30, 35Q35, 37N15, 76D05, Structure (category theory), Motion (geometry), Fluid mechanics, 01 natural sciences, Domain (mathematical analysis), 010101 applied mathematics, Physics::Fluid Dynamics, Classical mechanics, incompressible Navier-Stokes equations, Fluid–structure interaction, Fluid-structure interaction, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Uniqueness, Boundary value problem, 0101 mathematics, Mathematics
Abstract: International audience; In this paper we study a three-dimensional fluid-structure interaction problem. The motion of the fluid is modeled by the Navier-Stokes equations and we consider for the elastic structure a finite dimensional approximation of the equation of linear elasticity. The time variation of the fluid domain is not known a priori, so we deal with a free boundary value problem. Our main result yields the local in time existence and uniqueness of strong solutions for this system.
Published: 2012
Full Text: View/download PDF

31. Weak solutions for the motion of a self-propelled deformable structure in a viscous Incompressible fluid

Author: Takéo Takahashi, Marius Tucsnak, Šárka Nečasová, Mathematical Institute [Praha] - Academy of Sciences, Czech Academy of Sciences [Prague] (CAS), Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est
Subjects: Physics, Partial differential equation, Deformation (mechanics), Applied Mathematics, 010102 general mathematics, Motion (geometry), Equations of motion, Mechanics, 01 natural sciences, Physics::Fluid Dynamics, 010101 applied mathematics, Classical mechanics, Position (vector), Fluid–structure interaction, Free boundary problem, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Navier–Stokes equations, ComputingMilieux_MISCELLANEOUS
Abstract: We consider the three-dimensional motion of a self-propelled deformable structure into a viscous incompressible fluid. The deformation of the solid is given whereas its position is unknown. Such a system could model the propulsion of fish-like swimmers. The equations of motion of the fluid are the Navier-Stokes equations and the equations for the structure are deduced from Newton's laws. The corresponding system is a free boundary problem and the main result of the paper is the existence of weak solutions for this problem.
Published: 2011
Full Text: View/download PDF

32. Inverse problem and null-controllability for parabolic systems

Author: Takéo Takahashi, Galina C. García, Departamento de Matemática y Ciencia de la Computación, Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Robust control of infinite dimensional systems and applications (CORIDA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), and CORIDA
Subjects: Generalized inverse, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Null (mathematics), Boundary (topology), Inverse problem, controllability, 01 natural sciences, Parabolic partial differential equation, 010101 applied mathematics, Controllability, Inverse scattering problem, inverse problem, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Initial value problem, 0101 mathematics, 93C25, 93B07, 93B05, 93C20, 35R30, Mathematics
Abstract: In this paper, we present some abstract results giving a general connection between null-controllability and several inverse problems for a class of parabolic equations. We obtain some conditional stability estimates for the inverse problems consisting of determining the initial condition and the source term, from interior or boundary measurements. We apply this framework for Stokes system with interior and boundary observations, for a coupling of two Stokes system and a linear fluid-structure system.
Published: 2011
Full Text: View/download PDF

33. Homogenization and singular limits for the complete Navier-Stokes-Fourier system

Author: Eduard Feireisl, Takéo Takahashi, Antonin Novotny, Mathematical Institute [Praha] - Academy of Sciences, Czech Academy of Sciences [Prague] (CAS), Institut de Mathématiques de Toulon - EA 2134 (IMATH), Université de Toulon (UTLN), Institut Élie Cartan de Nancy (IECN), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria), Robust control of infinite dimensional systems and applications (CORIDA), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), CORIDA, Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Czech Academy of Sciences [Prague] ( ASCR ), Institut de Mathématiques de Toulon - EA 2134 ( IMATH ), Université de Toulon ( UTLN ), Institut Élie Cartan de Nancy ( IECN ), Institut National de Recherche en Informatique et en Automatique ( Inria ) -Université Henri Poincaré - Nancy 1 ( UHP ) -Université Nancy 2-Institut National Polytechnique de Lorraine ( INPL ) -Centre National de la Recherche Scientifique ( CNRS ), Robust control of infinite dimensional systems and applications ( CORIDA ), Institut National de Recherche en Informatique et en Automatique ( Inria ) -Université Henri Poincaré - Nancy 1 ( UHP ) -Université Nancy 2-Institut National Polytechnique de Lorraine ( INPL ) -Centre National de la Recherche Scientifique ( CNRS ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Université Henri Poincaré - Nancy 1 ( UHP ) -Université Nancy 2-Institut National Polytechnique de Lorraine ( INPL ) -Centre National de la Recherche Scientifique ( CNRS ) -Laboratoire de Mathématiques et Applications de Metz ( LMAM ), Université Paul Verlaine - Metz ( UPVM ) -Centre National de la Recherche Scientifique ( CNRS ) -Université Paul Verlaine - Metz ( UPVM ) -Centre National de la Recherche Scientifique ( CNRS ) -Inria Nancy - Grand Est, and Institut National de Recherche en Informatique et en Automatique ( Inria )
Subjects: Mathematics(all), Compressible Navier-Stokes-Fourier equations, General Mathematics, Viscous liquid, 01 natural sciences, Homogenization (chemistry), Compressible flow, Physics::Fluid Dynamics, symbols.namesake, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Mathematics, Homogenization, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Porous medium equation, 010101 applied mathematics, Nonlinear system, Fourier transform, Fourier analysis, symbols, Compressibility, Porous medium, Compressible Navier–Stokes–Fourier equations
Abstract: International audience; In this paper we apply the methods of homogenization to the full Navier-Stokes-Fourier system describing the motion of a general viscous, compressible, and heat conducting fluid. We study the asymptotic behavior of solutions in perforated domains with tiny holes, where the diameter of the holes is proportional to their mutual distance. As a limit system, we identify a porous medium type equation with a nonlinear Darcy's law.
Published: 2010
Full Text: View/download PDF

34. Blow up and grazing collision in viscous fluid solid interaction systems

Author: Matthieu Hillairet, Takéo Takahashi, Mathématiques pour l'Industrie et la Physique (MIP), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Robust control of infinite dimensional systems and applications (CORIDA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria), and Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques et Applications de Metz (LMAM)
Subjects: Applied Mathematics, 010102 general mathematics, Mathematics::Analysis of PDEs, Interaction systems, Viscous liquid, Viscous incompressible fluid, Collision, 01 natural sciences, 010101 applied mathematics, Strong solutions, Physics::Fluid Dynamics, Classical mechanics, Bounded function, Compressibility, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Ball (mathematics), 0101 mathematics, Mathematical Physics, Analysis, Mathematics
Abstract: International audience; In this paper we investigate finite time blow up of strong solutions to the system describing the motion of a rigid ball inside a bounded cavity filled with a viscous incompressible fluid. The equations of motion for the fluid are of Navier--Stokes type and the equations for the motion of the rigid ball are obtained by applying Newton's laws. The whole system evolves under the action of gravity. First, we prove contact between the ball and the boundary of the cavity implies the blow up of the strong solution. Then we prove for some configurations such a contact has to occur in finite time.
Published: 2010
Full Text: View/download PDF

35. Small solids in an inviscid fluid

Author: Takéo Takahashi, Nicolas Seguin, Frédéric Lagoutière, Boris Andreianov, Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC), Laboratoire de Recherche en Informatique (LRI), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Robust control of infinite dimensional systems and applications (CORIDA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), CORIDA, Université de Bourgogne (UB)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria), and Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques et Applications de Metz (LMAM)
Subjects: Statistics and Probability, Solid-fluid interaction, 01 natural sciences, symbols.namesake, Quadratic equation, 35F25, 35L80, 65M99, Inviscid flow, singular source term, well-balanced scheme, random-choice method, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, adapted entropy, Mathematics, Partial differential equation, Finite volume method, Applied Mathematics, 010102 general mathematics, Mathematical analysis, General Engineering, Riemann solver, Computer Science Applications, Burgers' equation, Burgers equation, 010101 applied mathematics, Drag, Ordinary differential equation, symbols
Abstract: We present in this paper several results concerning a simple model of interaction between an inviscid fluid, modeled by the Burgers equation, and a particle, assumed to be point-wise. It is composed by a first-order partial differential equation which involves a singular source term and by an ordinary differential equation. The coupling is ensured through a drag force that can be linear or quadratic. Though this model can be considered as a simple one, its mathematical analysis is involved. We put forward a notion of entropy solution to our model, define a Riemann solver and make first steps towards well-posedness results. The main goal is to construct easy-to-implement and yet reliable numerical approximation methods; we design several finite volume schemes, which are analyzed and tested.
Published: 2010
Full Text: View/download PDF

36. Solving inverse source problems using observability. Applications to the Euler-Bernoulli plate equation

Author: Ana L. Silvestre, Carlos J.S. Alves, Takéo Takahashi, Marius Tucsnak, Instituto Superior Técnico, Universidade Técnica de Lisboa (IST), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Robust control of infinite dimensional systems and applications (CORIDA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est
Subjects: 0209 industrial biotechnology, Control and Optimization, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Boundary (topology), Inverse, Observable, 02 engineering and technology, 01 natural sciences, Bernoulli's principle, symbols.namesake, 020901 industrial engineering & automation, Euler's formula, symbols, Identifiability, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Point (geometry), Observability, 0101 mathematics, Mathematics
Abstract: The aim of this paper is to provide a general framework for solving a class of inverse source problems by using exact observability of infinite dimensional systems. More precisely, we show that if a system is exactly observable, then a source term in this system can be identified by knowing its intensity and appropriate observations which often correspond to measurements of some boundary traces. This abstract theory is then applied to obtain new identifiability results for a system governed by the Euler-Bernoulli plate equation. Using a different methodology, we show that exact observability can be used to identify both the locations and the intensities of combinations of point sources in the plate equation.
Published: 2009
Full Text: View/download PDF

37. Topological sensitivity analysis for time-dependent problems

Author: Samuel Amstutz, Boris Vexler, Takéo Takahashi, Laboratoire d'Analyse non linéaire et Géométrie (LANLG), Avignon Université (AU), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Robust control of infinite dimensional systems and applications (CORIDA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences (OeAW), CORIDA, and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est
Subjects: Control and Optimization, 010102 general mathematics, Topology optimization, parabolic equations, Topological space, Topology, 01 natural sciences, Domain (mathematical analysis), hyperbolic equations, 010101 applied mathematics, Computational Mathematics, 49Q10, 49Q12, 35K05, 35L05, Control and Systems Engineering, Topological sensitivity, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], General topology, Sensitivity (control systems), 0101 mathematics, Particular point topology, Topological quantum number, Topology (chemistry), ComputingMilieux_MISCELLANEOUS, topology optimization, Mathematics
Abstract: The topological sensitivity analysis consists in studying the behavior of a given shape functional when the topology of the domain is perturbed, typically by the nucleation of a small hole. This notion forms the basic ingredient of different topology optimization/reconstruction algorithms. From the theoretical viewpoint, the expression of the topological sensitivity is well-established in many situations where the governing p.d.e. system is of elliptic type. This paper focuses on the derivation of such formulas for parabolic and hyperbolic problems. Different kinds of cost functionals are considered.
Published: 2008
Full Text: View/download PDF

38. Convergence of a Lagrange--Galerkin method for a fluid-rigid body system in ALE formulation

Author: Guillaume Legendre, Takéo Takahashi, CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), The work of the first author was supported by FONDECYT under grant n° 3060018 and by the Centro de Modelamiento Matemático., Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), and Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM)
Subjects: Mathematical optimization, 010103 numerical & computational mathematics, 01 natural sciences, Physics::Fluid Dynamics, Method of characteristics, Convergence (routing), Fluid–structure interaction, Fluid-structure interaction, Arbitrary Lagrangian Eulerian, Applied mathematics, Lagrange–Galerkin method, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Galerkin method, Mathematics, Numerical Analysis, Partial differential equation, Applied Mathematics, Numerical analysis, Rigid body, Finite element method, 010101 applied mathematics, Computational Mathematics, Modeling and Simulation, Incompressible Navier–Stokes equations, Analysis
Abstract: International audience; In this paper, we propose a numerical scheme to compute the motion of a two-dimensional rigid body in a viscous fluid, modeled by the Navier-Stokes equations. Our method combines a finite element approximations and the use of the method of characteristics to solve an Arbitrary Lagrangian Eulerian formulation of the problem. We derive error estimates for this scheme which imply its convergence.
Published: 2008
Full Text: View/download PDF

39. Uniformly exponentially stable approximations for a class of second order evolution equations. Application to LQR optimization problems

Author: Karim Ramdani, Takéo Takahashi, Marius Tucsnak, Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Robust control of infinite dimensional systems and applications (CORIDA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est
Subjects: 0209 industrial biotechnology, Control and Optimization, Discretization, hp-FEM, 02 engineering and technology, Linear-quadratic regulator, 01 natural sciences, Algebraic Riccati equation, 020901 industrial engineering & automation, Exponential stability, Riccati equation, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Mathematics, finite difference, 010102 general mathematics, Mathematical analysis, Finite difference, 93D15, 65M60, 65M12, Finite element method, uniform exponential stability, Computational Mathematics, Control and Systems Engineering, finite element, LQR optimal control problem, wave equation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: A paraître dans ESAIM COCV; International audience; We consider the approximation of a class of exponentially stable infinite dimensional linear systems modelling the damped vibrations of one dimensional vibrating systems or of square plates. It is by now well known that the approximating systems obtained by usual finite element or finite difference are not, in general, uniformly stable with respect to the discretization parameter. Our main result shows that, by adding a suitable numerical viscosity term in the numerical scheme, our approximations are uniformly exponentially stable. This result is then applied to obtain strongly convergent approximations of the solutions of the algebraic Riccati equations associated to an LQR optimal control problem. We next give an application to a non-homogeneous string equation. Finally we apply similar techniques for approximating the equations of a damped square plate.
Published: 2007
Full Text: View/download PDF

40. On the motion of a rigid body immersed in a bidimensional incompressible perfect fluid

Author: Jaime H. Ortega, Lionel Rosier, Takéo Takahashi, Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Centre de modélisation mathématique (CMM), and Universitad de Chile-Centre National de la Recherche Scientifique (CNRS)
Subjects: Conservation law, Angular momentum, Applied Mathematics, 010102 general mathematics, Perfect fluid, Vorticity, Rigid body, 01 natural sciences, Euler equations, Physics::Fluid Dynamics, 010101 applied mathematics, Euler's laws of motion, symbols.namesake, Classical mechanics, Fluid–structure interaction, symbols, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Mathematical Physics, Analysis, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract: We consider the motion of a rigid body immersed in a bidimensional incompressible perfect fluid. The motion of the fluid is governed by the Euler equations and the conservation laws of linear and angular momentum rule the dynamics of the rigid body. We prove the existence and uniqueness of a global classical solution for this fluid–structure interaction problem. The proof relies mainly on weighted estimates for the vorticity associated with the strong solution of a fluid–structure interaction problem obtained by incorporating some viscosity.
Published: 2007
Full Text: View/download PDF

41. Wellposedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid

Author: Patricio Cumsille, Takéo Takahashi, Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Centro de Modelamiento Matemático [Santiago] (CMM), and Universidad de Santiago de Chile [Santiago] (USACH)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Conservation law, General Mathematics, 010102 general mathematics, Mathematical analysis, Geometry, Fluid mechanics, Reynolds stress, Viscous liquid, Rigid body, 01 natural sciences, Physics::Fluid Dynamics, 010101 applied mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Boundary value problem, 0101 mathematics, Navier–Stokes equations, Poinsot's ellipsoid, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract: In this paper, we consider the interaction between a rigid body and an incompressible, homogeneous, viscous fluid. This fluid-solid system is assumed to fill the whole space ℝd, d = 2 or 3. The equations for the fluid are the classical Navier-Stokes equations whereas the motion of the rigid body is governed by the standard conservation laws of linear and angular momentum. The time variation of the fluid domain (due to the motion of the rigid body) is not known a priori, so we deal with a free boundary value problem.
Published: 2007

42. A uniformly stable finite difference space semi-discretization for the internal stabilization of the plate equation in a square

Author: Marius Tucsnak, Takéo Takahashi, Karim Ramdani, Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Robust control of infinite dimensional systems and applications (CORIDA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est
Subjects: Discretization, 010102 general mathematics, Mathematical analysis, Finite difference, Finite difference coefficient, 010103 numerical & computational mathematics, Space (mathematics), 01 natural sciences, Square (algebra), Scheme (mathematics), [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Exponential decay, Plate equation, ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract: International audience; We propose a finite difference space semi-discretization of the stabilized Bernoulli-Euler plate equation in a square. The scheme studied yields a uniform exponential decay rate with respect to the mesh size.
Published: 2006
Full Text: View/download PDF

43. A Control Theoretic Approach to the Swimming of Microscopic Organisms

Author: Marius Tucsnak, Takéo Takahashi, Jorge San Martín, Takahashi, Takéo, Centre de Modélisation Mathématique / Centro de Modelamiento Matemático (CMM), Centre National de la Recherche Scientifique (CNRS), Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Centre de modélisation mathématique (CMM), and Universitad de Chile-Centre National de la Recherche Scientifique (CNRS)
Subjects: Applied Mathematics, 010102 general mathematics, Relative velocity, Boundary (topology), Reynolds number, Thrust, Fluid mechanics, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Rigid body, 01 natural sciences, 010101 applied mathematics, symbols.namesake, Classical mechanics, Position (vector), symbols, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Vector field, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Mathematics
Abstract: Papier accepté pour la publication dans Quarterly of Applied Mathematics; International audience; In this paper, we give a control theoretic approach to the slow self-propelled motion of a rigid body in a viscous fluid. The control of the system is the relative velocity of the fluid with respect to the solid on the boundary of the rigid body (the thrust). Our main results show that, there exists a large class of finite dimensional input spaces for which the system is exactly controllable, i.e., one can find controls steering the rigid body in any final position with a prescribed velocity field. The equations we use are motivated by models of swimming of micro-organisms like cilia. We give a control theoretic interpretation of the swimming mechanism of these organisms, which takes place at very low Reynolds numbers. Our aim is to give a control theoretic interpretation of the swimming mechanism of micro-organisms (like ciliata) which is one of the fascinating problems in fluid mechanics.
Published: 2006

44. Internal stabilization of the plate equation in a square : the continuous and the semi-discretized problems

Author: Karim Ramdani, Marius Tucsnak, Takéo Takahashi, Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Robust control of infinite dimensional systems and applications (CORIDA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est
Subjects: Mathematics(all), 0209 industrial biotechnology, Discretization, General Mathematics, 02 engineering and technology, 01 natural sciences, Square (algebra), 93D15, 65M60, 65M12, symbols.namesake, 020901 industrial engineering & automation, Exponential stability, Uniform exponential stability, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Exponential decay, Mathematics, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Finite difference, Finite difference method, Stabilization, Euler equations, Finite-difference, Plate equation, Frequency domain, symbols, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract: National audience; This paper is devoted to the study of the internal stabilization of the Bernoulli-Euler plate equation in a square. The continuous and the space semi-discretizated problems are successively considered and analyzed using a frequency domain approach. For the infinite dimensional problem, we provide a new proof of the exponential stability result, based on a two dimensional Ingham's type result. In the second and main part of the paper, we propose a finite difference space semi-discretization scheme and we prove that this scheme yields a uniform exponential decay rate (with respect to the mesh size).
Published: 2006
Full Text: View/download PDF

45. FLUID-RIGID STRUCTURE INTERACTION SYSTEM WITH COULOMB'S LAW.

Author: BĂLILESCU, LOREDANA, SAN MARTIN, JORGE, and TAKÉO TAKAHASHI
Subjects: RIGID bodies, BOUNDARY value problems, COULOMB'S law, DIRICHLET principle, NAVIER-Stokes equations, CAUCHY problem
Abstract: We propose a new model in a fluid-rigid structure system composed by a rigid body and a viscous incompressible fluid using a boundary condition based on Coulomb's law. This boundary condition allows the fluid to slip on the boundary if the tangential component of the stress is too large. In the opposite case, we recover the standard Dirichlet boundary condition. The governing equations are the Navier-Stokes system for the fluid and the Newton laws for the body. The corresponding coupled system can be written as a variational inequality. We prove that there exists a weak solution of this system. [ABSTRACT FROM AUTHOR]
Published: 2017
Full Text: View/download PDF

46. Global strong solutions for the two-dimensional motion of an infinite cylinder in a viscous fluid

Author: Takéo Takahashi, Marius Tucsnak, Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Tucsnak, Marius, and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est
Subjects: Physics, Conservation law, Angular momentum, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Dynamics (mechanics), Viscous liquid, Condensed Matter Physics, Rigid body, 01 natural sciences, Physics::Fluid Dynamics, 010101 applied mathematics, Computational Mathematics, Classical mechanics, Cylinder, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Uniqueness, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Poinsot's ellipsoid, Mathematical Physics
Abstract: In this paper, we consider a two-dimensional fluid-rigid body problem. The motion of the fluid is modelled by the Navier-Stokes equations, whereas the dynamics of the rigid body is governed by the conservation laws of linear and angular momentum. The rigid body is supposed to be an infinite cylinder of circular cross-section. Our main result is the existence and uniqueness of global strong solutions.
Published: 2005

47. Liquid jet generation and break-up

Author: Céline Baranger, Gérard Baudin, Laurent Boudin, Bruno Després, Frédéric Lagoutière, Emmanuel LAPEBIE, Takéo Takahashi, Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Centre de Mathématiques et de Leurs Applications (CMLA), École normale supérieure - Cachan (ENS Cachan)-Centre National de la Recherche Scientifique (CNRS), Centre d'étude de Gramat (CEG), Délégation Générale pour l'Armement, Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est
Subjects: Physics::Fluid Dynamics, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; This work is motivated by the numerical simulation of the generation and break-up of droplets after the impact of a rigid body on a tank filled with a compressible fluid. This paper splits into two very different parts. The first part deals with the modeling and the numerical resolution of a spray of liquid droplets in a compressible medium like air. Phenomena taken into account are the breakup effects due to the velocity and pressure waves in the compressible ambient fluid. The second part is concerned with the transport of a rigid body in a compressible liquid, involving reciprocal effects between the two components. A new one-dimensional algorithm working on a fixed Eulerian mesh is proposed.
Published: 2005
Full Text: View/download PDF

48. Convergence of the Lagrange-Galerkin method for the Equations Modelling the Motion of a Fluid-Rigid System

Author: Jean-François Scheid, Takéo Takahashi, Marius Tucsnak, Jorge San Martín, Departamento de Ingeniería Matemática [Santiago] (DIM), Universidad de Chile = University of Chile [Santiago] (UCHILE)-Centre National de la Recherche Scientifique (CNRS), Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Universidad de Chile = University of Chile [Santiago] (UCHILE)
Subjects: finite element method, 35Q30, 76D05, 65M12, 76M10, fluid-structure interaction, 010103 numerical & computational mathematics, 01 natural sciences, Physics::Fluid Dynamics, symbols.namesake, Multigrid method, Simultaneous equations, Collocation method, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Mathematics, Numerical Analysis, Independent equation, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Lagrange-Galerkin method, 16. Peace & justice, Euler equations, Computational Mathematics, Nonlinear system, incompressible Navier-Stokes equations, symbols, Differential algebraic equation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Numerical partial differential equations
Abstract: In this paper, we consider a Lagrange--Galerkin scheme to approximate a two-dimensional fluid-rigid body problem. The equations of the system are the Navier--Stokes equations in the fluid part, coupled with ordinary differential equations for the dynamics of the rigid body. In this problem, the equations of the fluid are written in a domain whose variation is one of the unknowns. We introduce a numerical method based on the use of characteristics and on finite elements with a fixed mesh. Our main result asserts the convergence of this scheme.
Published: 2005
Full Text: View/download PDF

49. Classical solutions for the equations modelling the motion of a ball in a bidimensional incompressible perfect fluid

Author: Lionel Rosier, Takéo Takahashi, Jaime H. Ortega, Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Centre de modélisation mathématique (CMM), and Universitad de Chile-Centre National de la Recherche Scientifique (CNRS)
Subjects: Numerical Analysis, Partial differential equation, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Perfect fluid, Vorticity, 01 natural sciences, Euler equations, Physics::Fluid Dynamics, 010101 applied mathematics, Computational Mathematics, symbols.namesake, Modeling and Simulation, symbols, Fluid dynamics, Compressibility, Uniqueness, Ball (mathematics), 0101 mathematics, [MATH]Mathematics [math], Analysis, Mathematics
Abstract: In this paper we investigate the motion of a rigid ball in an incompressible perfect fluid occupying R 2 . We prove the global in time existence and the uniqueness of the classical solution for this fluid-structure problem. The proof relies mainly on weighted estimates for the vorticity associated with the strong solution of a fluid-structure problem obtained by incorporating some dissipation.
Published: 2005
Full Text: View/download PDF

50. Analysis of strong solutions for the equations modeling the motion of a rigid-fluid system in a bounded domain

Author: Takéo Takahashi
Subjects: 76D03, Applied Mathematics, 35Q30, Analysis, 76D05
Abstract: In this paper, we study a fluid--rigid-body interaction problem. The motion of the fluid is modeled by the Navier-Stokes equations, written in an unknown bounded domain depending on the displacement of the rigid body. Our main result yields existence and uniqueness of strong solutions. In the two-dimensional case, the solutions are global provided that the rigid body does not touch the boundary. In the three-dimensional case, we obtain local-in-time existence and global existence for small data. Moreover, we prove an asymptotic stability result.
Published: 2003

Catalog

Books, media, physical & digital resources

See catalog results

Searchworks

Select search scope, currently: Articles Catalog books, media & more in Jio Institute collections Articles journal articles & other e-resources

Search

Search Constraints

Refine your results

Search Limiters

Topic

Publication Year Range

Publication Type

Journal

Database

Publisher

72 results on '"Takéo Takahashi"'

Search Results

Catalog

Select search scope, currently: Articles

Catalog

books, media & more in Jio Institute collections

Articles

journal articles & other e-resources