Global Lipschitz stability of multiple space dependent ionic parameters in cardiac electrophysiology
Résumé
This paper is devoted to analyze the inverse problem of determining two space dependent ionic parameters of a nonlinear reaction diffusion system described by a parabolic-elliptic one, modeling the electrical activity in the heart. We consider the classical phenomenological model in cardiac electrophysiology of FitzHugh-Nagumo to describe the ionic exchanges at the microscopic level. Our main result is the uniqueness and a Lipschitz stability estimate for two ionic parameters (k, γ) of the model using sub-boundary observations over an interval of time. The key ingredients are global Carleman-type estimates with a suitable observations acting on a part of the boundary.
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