Carleman estimate for a linearized bidomain model in electrocardiology and its applications

This paper concerns Carleman estimate and its applications for a linearized bidomain model in electrocardiology, which describes the electrical activity in the cardiac tissue. We first establish a new Carleman estimate for this reaction-diffusion system. By means of this Carleman estimate, we study two problems for the linearized bidomian model, a Cauchy problem and an inverse conductivities problem. We prove a conditional stability result for the Cauchy problem and a Holder stability result for the inverse conductivities problem.