Stability results for the parameter identification inverse problem in cardiac electrophysiology

In this paper we prove a stability estimate of the parameter identification problem in cardiac electrophysiology modeling. We use the monodomain model which is a reaction diffusion parabolic equation where the reaction term is obtained by solving an ordinary differential equation (ODE). We are interested in proving the stability of the identification of the parameter ${\tau }_{in}$, which is the parameter that multiplies the cubic term in the reaction term. The proof of the result is based on a new Carleman-type estimate for both partial differential equation (PDE) and ODE problems. As a consequence of the stability result we prove the uniqueness of the parameter ${\tau }_{in}$ giving some observations of both state variables at a given time t ₀ in the whole domain and in the PDE variable in a non empty open subset w ₀ of the domain. (paper)