Application of the $j$-subgradient in a problem of electropermeabilisation

TL;DR

This paper investigates a coupled elliptic-parabolic system modeling electrical activity in biological tissues, demonstrating its gradient structure via the $j$-subgradient, which aids in proving well-posedness and guiding numerical discretization.

Contribution

It introduces the use of the $j$-subgradient to establish the gradient structure and well-posedness of a complex biological tissue model.

Findings

The system has a gradient structure due to the $j$-subgradient.

The approach enables effective discretization of the model.

Numerical experiments validate the theoretical results.

Abstract

We study a coupled elliptic-parabolic Poincar\'e-Steklov system arising in electrical cell activity in biological tissues. By using the notion of $j$-subgradient, we show that this system has a gradient structure and thus obtain wellposedness. We further exploit the gradient structure for the discretisation of the problem and provide numerical experiments.