The bidomain problem as a gradient system

TL;DR

This paper studies a nonlinear bidomain system, leveraging its gradient structure and $j$-subgradient concept to establish well-posedness in the energy space and present initial numerical experiments.

Contribution

It introduces a novel approach using the gradient system framework and $j$-subgradient to analyze the nonlinear bidomain problem, proving well-posedness.

Findings

Proved well-posedness of the nonlinear bidomain system in the energy space.

Established the gradient structure and $j$-subgradient framework for the system.

Presented initial numerical experiments demonstrating the approach.

Abstract

We consider a general, nonlinear version of the bidomain system. Using the gradient structure of this system, but also the notion of $j$-subgradient, we prove wellposedness of the bidomain system in the energy space and provide first numerical experiments.