Strong solutions and asymptotic behavior of bidomain equations with random noise

TL;DR

This paper investigates the existence, behavior, and stability of strong solutions to stochastic bidomain equations, including their asymptotic properties and invariant measures, under random noise influences.

Contribution

It provides new conditions for strong solution existence and analyzes the asymptotic and invariant measure properties of stochastic bidomain equations.

Findings

Existence of local and global strong solutions established.

Analysis of asymptotic behavior under stochastic perturbations.

Characterization of the support of the invariant measure.

Abstract

In this paper we study the conditions for the existence of strong solutions (both local and global) for stochastic bidomain equations. To this end, we use apriori energy estimates and Serrin-type theorems. We further address the asymptotic behavior of the solutions, which includes the analysis of small stochastic perturbations and large deviations. In a separate section we specify the support of the invariant measure.