Partial Differential Equations/Optimal Control
Null controllability of a degenerated reaction–diffusion system in cardiac electro-physiology
Comptes Rendus. Mathématique, Volume 350 (2012) no. 11-12, pp. 587-590.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2012.06.006
Bendahmane, Mostafa 1; Chaves-Silva, Felipe Wallison 2

1 Laboratoire de institut mathematiques de Bordeaux, Université Victor-Segalen Bordeaux 2, place de la Victoire, 33076 Bordeaux, France
2 BCAM – Basque Center for Applied Mathematics, Alameda Mazzaredo 14, 48009 Bilbao, Basque Country, Spain
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Bendahmane, Mostafa; Chaves-Silva, Felipe Wallison. 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. http://www.numdam.org/articles/10.1016/j.crma.2012.06.006/

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