Strong solutions and asymptotic behavior of bidomain equations with random noise

Author:

Kapustyan Oleksiy1,Misiats Oleksandr2,Stanzhytskyi Oleksandr1

Affiliation:

1. Department of Mathematics, Taras Shevchenko National University of Kyiv, Ukraine

2. Department of Mathematics, Virginia Commonwealth University, Richmond, VA 23284, USA

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 a priori 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, whose existence was established in [M. Hieber, O. Misiats and O. Stanzhytskyi, On the bidomain equations driven by stochastic forces, Discrete Contin. Dyn. Syst. 40 (11) (2020) 6159–6177].

Funder

Simons Foundation

State Agency for Science, Innovations and Informatization of Ukraine

Publisher

World Scientific Pub Co Pte Ltd

Subject

Modeling and Simulation

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