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In this paper we show the global well-posedness of solutions to a three-dimensional magnetohydrodynamical (MHD) model in porous media. Compared to the classical MHD equations, our system involves a nonlinear damping term in the momentum equations due to the "Brinkman-Forcheimerextended-Darcy" law of ow in porous media.

We consider three-dimensional (3D) Boussinesq convection system of an incompressible fluid in a closed sample of a porous medium. Specifically, we introduce and analyze a 3D Brinkman-Forchheimer-Bénard convection problem describing the behavior of an incompressible fluid in a porous medium between two plates heated from the bottom and cooled from the top. We show the existence and uniqueness of global in-time solutions, and the existence of absorbing balls in $ L^2 $ and $ H^1 $. Eventually, we comment on the applicability of a data assimilation algorithm to our system. [ABSTRACT FROM AUTHOR]

In this paper we introduce and analyze an algorithm for continuous data assimilation for a three-dimensional Brinkman-Forchheimer-extended Darcy (3D BFeD) model of porous media. This model is believed to be accurate when the flow velocity is too large for Darcy's law to be valid, and additionally the porosity is not too small. The algorithm is inspired by ideas developed for designing finite-parameters feedback control for dissipative systems. It aims to obtain improved estimates of the state of the physical system by incorporating deterministic or noisy measurements and observations. Specifically, the algorithm involves a feedback control that nudges the large scales of the approximate solution toward those of the reference solution associated with the spatial measurements. In the first part of the paper, we present a few results of existence and uniqueness of weak and strong solutions of the 3D BFeD system. The second part is devoted to the convergence analysis of the data assimilation algorithm.

This paper is dedicated to the setting and analysis of an optimal control problem for a two-phase system composed of two non-linearly coupled Chan–Hilliard-type equations. The model describes the evolution of a tumor cell fraction and a nutrient-rich extracellular water volume fraction. The main objective of this paper is the identification of the system's physical parameters, such as the viscosities and the proliferation rate, in addition to the controllability of the system's unknowns. For this purpose, we introduce an adequate cost function to be optimized by analyzing a linearized system, deriving the adjoint system, and defining the optimality condition. Eventually, we provide a numerical simulation example illustrating the theoretical results. Finally, numerical simulations of a tumor growing in two and three dimensions are carried out in order to illustrate the evolution of such a clinical situation and to possibly suggest different treatment strategies. [ABSTRACT FROM AUTHOR]

The structure and properties of poly(deamino-tyr-tyr carbonate hexyl ester), in dilute and semidilute solutions, were studied using static, dynamic light scattering, and viscometry. The overlap concentration, c* is determined by viscosity. The angular dependence of Zimm plots shows no downturn at low angles. In addition, bimodal distribution curves were computed from the quasielastic measurements. The radius of gyration and the second virial coefficient [A.sub.2] are found to be respectively 45.8 nm and 9.4 mol [cm.sup.3] [g.sup.-2]. The correlation and persistence lengths are discussed. The poly (deamino-tyr-tyr carbonate hexyl ester) or poly(DTH-carbonate) chain in THF, at T = 20°C, behaves as a wormlike chain with persistence length. The persistence length obtained using light scattering is compared with that obtained using viscosity with good agreement. These values obtained from these measurements reflect a high degree of local chain persistence. The reduced viscosity in dilute regime provides a value of apparent viscosity hydrodynamic radius three times lower than obtained by static light scattering. POLYM. ENG. SCI., 50:1605-1612, 2010. [C] 2010 Society of Plastics Engineers, INTRODUCTION Polyaminoacides are frequently employed in many industrial and pharmaceutical applications. They represent a research field of large interest in science and technology and are a common domain for physics, [...]

In this paper we show the global well-posedness of solutions to a three-dimensional magnetohydrodynamical (MHD) model in porous media. Compared to the classical MHD equations, our system involves a nonlinear damping term in the momentum equations due to the "Brinkman-Forcheimer-extended-Darcy" law of flow in porous media. [ABSTRACT FROM AUTHOR]

This paper is devoted to the mathematical analysis of a class of nonlinear fractional Schrödinger equations with a general Hartree-type integrand. We show the well-posedness of the associated Cauchy problem and prove the existence and stability of standing waves under suitable assumptions on the nonlinearity. Our proofs rely on a contraction argument in mixed functional spaces and the concentration-compactness method. [ABSTRACT FROM AUTHOR]