Asymptotic decay under nonlinear and noncoercive dissipative effects for electrical conduction in biological tissues

TL;DR

This paper proves that solutions to a nonlinear model of electrical conduction in biological tissues converge to a periodic state over time, even with noncoercive nonlinearities, for both homogenized and non-homogenized cases.

Contribution

It establishes asymptotic convergence to periodic solutions in a nonlinear, noncoercive setting, extending previous results to more general biological tissue models.

Findings

Solutions converge to periodic states over time

The model handles noncoercive nonlinearities

Results apply to both homogenized and non-homogenized models

Abstract

We consider a nonlinear model for electrical conduction in biological tissues. The nonlinearity appears in the interface condition prescribed on the cell membrane. The purpose of this paper is proving asymptotic convergence for large times to a periodic solution when time-periodic boundary data are assigned. The novelty here is that we allow the nonlinearity to be noncoercive. We consider both the homogenized and the non-homogenized version of the problem.