1. Internal nonnegative stabilization for some parabolic equations
- Author
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Bedr'Eddine Ainseba, Sebastian Aniţa, 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), Tools of automatic control for scientific computing, Models and Methods in Biomathematics (ANUBIS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Institute of Mathematics 'Octav Mayer', Romanian Academy, 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), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Inria Bordeaux - Sud-Ouest
- Subjects
education.field_of_study ,Applied Mathematics ,Mathematical analysis ,Population ,General Medicine ,Parabolic cylinder function ,01 natural sciences ,Parabolic partial differential equation ,Domain (mathematical analysis) ,010305 fluids & plasmas ,010101 applied mathematics ,Elliptic operator ,Elliptic partial differential equation ,Parabolic cylindrical coordinates ,0103 physical sciences ,0101 mathematics ,education ,ComputingMilieux_MISCELLANEOUS ,Analysis ,Eigenvalues and eigenvectors ,Mathematics - Abstract
The internal zero-stabilization of the nonnegative solutions to some parabolic equations is investigated. We provide a necessary and a sufficient condition for nonnegative stabilizability in terms of the sign of the principal eigenvalue of a certain elliptic operator. This principal eigenvalue is related to the rate of the convergence of the solution. We give some evaluations of this principal eigenvalue with respect to the geometry of the domain and of the support of the control. A stabilization result for an age-dependent population dynamics with diffusion is also established.
- Published
- 2008
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