Well-posedness for a modified bidomain model describing bioelectric activity in damaged heart tissues

TL;DR

This paper establishes the mathematical well-posedness of a modified bidomain model that captures electrical activity in damaged heart tissues, addressing degeneracy and complex coupling issues.

Contribution

It proves existence and uniqueness of solutions for a novel bidomain model tailored to pathological cardiac tissue, using an abstract parabolic framework.

Findings

Existence of solutions is proven for the modified model.

Uniqueness of solutions is established under the new framework.

The model accounts for degeneracy and non-standard coupling in damaged tissues.

Abstract

We prove the existence and the uniqueness of a solution for a modified bidomain model, describing the electrical behaviour of the cardiac tissue in pathological situations. The leading idea is to reduce the problem to an abstract parabolic setting, which requires to introduce several auxiliary differential systems and a non-standard bilinear form. The main difficulties are due to the degeneracy of the bidomain system and to its non-standard coupling with a diffusion equation, accounting for the presence of the pathological zone in the heart tissue.