Stochastically forced cardiac bidomain model

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Bendahmane, M.¹  Karlsen, K. H.² 

[1] Univ Victor Segalen Bordeaux 2, CNRS, UMR 525, Inst Math Bordeaux, F-33076 Bordeaux, France

[2] Univ Oslo, Dept Math, POB 1053, N-0316 Oslo, Norway

关键词: Stochastic partial differential equation;    Reaction-diffusion system;    Degenerate;    Weak solution;    Existence;    Uniqueness;    Bidomain model;    Cardiac electric field;   

DOI  :  10.1016/j.spa.2019.03.001

来源: Elsevier

【 摘 要 】

The bidomain system of degenerate reaction-diffusion equations is a well-established spatial model of electrical activity in cardiac tissue, with reaction linked to the cellular action potential and diffusion representing current flow between cells. The purpose of this paper is to introduce a stochastically forced version of the bidomain model that accounts for various random effects. We establish the existence of martingale (probabilistic weak) solutions to the stochastic bidomain model. The result is proved by means of an auxiliary nondegenerate system and the Faedo-Galerkin method. To prove convergence of the approximate solutions, we use the stochastic compactness method and Skorokhod-Jakubowski a.s. representations. Finally, via a pathwise uniqueness result, we conclude that the martingale solutions are pathwise (i.e., probabilistic strong) solutions. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

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