On a resolvent estimate for bidomain operators and its applications

We study bidomain equations that are commonly used as a model to represent the electrophysiological wave propagation in the heart. We prove existence, uniqueness and regularity of a strong solution in Lp spaces. For this purpose we derive an L∞ resolvent estimate for the bidomain operator by using a contradiction argument based on a blow-up argument. Interpolating with the standard L2-theory, we conclude that bidomain operators generate C0-analytic semigroups in Lp spaces, which leads to construct a strong solution to a bidomain equation in Lp spaces.