[Nulle contrôlabilité dʼun système dégénéré de réaction–diffusion dans lʼélectique-physiologie du cœur]
Ce travail est consacré à lʼanalyse de la nulle contrôlabilité dʼun système dégénéré de réaction–diffusion non-linéaire modélisant lʼactivité électrique du cœur. Notre contrôle agit dans un sous-domaine fixe du domaine du coeur. Nous prouvons la nulle contrôlabilité de notre modèle en établissant en particulier une estimation de Carleman pour lʼéquation dégénéré. Des estimations globales de type Carleman et la régularité parabolique sont employées.
This Note is devoted to the analysis of the null controllability of a nonlinear reaction–diffusion system, approximating a parabolic–elliptic system, modeling electrical activity in the heart. The uniform, with respect to the degenerating parameter, null controllability of the approximating system by a single control force acting on a subdomain is shown. The proof needs a precise estimate with respect to the degenerating parameter and it is done combining Carleman estimates and energy inequalities.
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@article{CRMATH_2012__350_11-12_587_0,
author = {Mostafa Bendahmane and Felipe Wallison Chaves-Silva},
title = {Null controllability of a degenerated reaction{\textendash}diffusion system in cardiac electro-physiology},
journal = {Comptes Rendus. Math\'ematique},
pages = {587--590},
publisher = {Elsevier},
volume = {350},
number = {11-12},
year = {2012},
doi = {10.1016/j.crma.2012.06.006},
language = {en},
}
TY - JOUR AU - Mostafa Bendahmane AU - Felipe Wallison Chaves-Silva TI - Null controllability of a degenerated reaction–diffusion system in cardiac electro-physiology JO - Comptes Rendus. Mathématique PY - 2012 SP - 587 EP - 590 VL - 350 IS - 11-12 PB - Elsevier DO - 10.1016/j.crma.2012.06.006 LA - en ID - CRMATH_2012__350_11-12_587_0 ER -
%0 Journal Article %A Mostafa Bendahmane %A Felipe Wallison Chaves-Silva %T Null controllability of a degenerated reaction–diffusion system in cardiac electro-physiology %J Comptes Rendus. Mathématique %D 2012 %P 587-590 %V 350 %N 11-12 %I Elsevier %R 10.1016/j.crma.2012.06.006 %G en %F CRMATH_2012__350_11-12_587_0
Mostafa Bendahmane; Felipe Wallison Chaves-Silva. Null controllability of a degenerated reaction–diffusion system in cardiac electro-physiology. Comptes Rendus. Mathématique, Volume 350 (2012) no. 11-12, pp. 587-590. doi : 10.1016/j.crma.2012.06.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.06.006/
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[4] A further generalization of the Kakutani fixed point theorem, with applications to Nash equilibrium points, Proc. AMS, Volume 3 (1952) no. 9, pp. 170-174
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