Null controllability of a degenerated reaction-diffusion system in cardiac electro-physiology [Nulle contrôlabilité d'un système dégénéré de réaction-diffusion dans l'électique-physiologie du cœur]

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. © 2012 Académie des sciences