Strong time-periodic solutions to the bidomain equations with arbitrary large forces

Abstract

We prove the existence of strong time-periodic solutions to the bidomain equations with arbitrary large forces. We construct weak time-periodic solutions by a Galerkin method combined with Brouwer's fixed point theorem and a priori estimate independent of approximation. We then show their regularity so that our solution is a strong time-periodic solution in $L^2$ spaces. Our strategy is based on the weak-strong uniqueness method.