Global Lipschitz stability of multiple space dependent ionic parameters in cardiac electrophysiology

Hamza Ammar (1) , Moncef Mahjoub , Néjib Zemzemi

1 LR-LAMSIN-ENIT - Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]

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.

Mots clés: Parameter identification; Inverse problem; Reaction-diffusion equations; Carleman estimate; Uniqueness; Stability result

Domaines: Equations aux dérivées partielles [math.AP]

Hamza Ammar, Moncef Mahjoub, Néjib Zemzemi. Global Lipschitz stability of multiple space dependent ionic parameters in cardiac electrophysiology. 2022. ⟨hal-03710817⟩