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].
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