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

TL;DR

This paper proves the existence of strong time-periodic solutions to the bidomain equations under large forces, using Galerkin methods, fixed point theorems, and regularity analysis.

Contribution

It introduces a novel approach combining Galerkin methods and weak-strong uniqueness to establish strong solutions for the bidomain equations with large forces.

Findings

Existence of strong time-periodic solutions for the bidomain equations.

Construction of weak solutions via Galerkin and Brouwer's fixed point theorem.

Verification of regularity to upgrade weak solutions to strong solutions.

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.