Regular dynamics for stochastic Fitzhugh-Nagumo systems with additive noise on thin domains

Abstract

<p style='text-indent:20px;'>This paper is devoted to bi-spatial random attractors of the stochastic Fitzhugh-Nagumo equations with additive noise on thin domains when the terminate space is the Sobolev space. We first established the existence of random attractor on regular space and then show that the upper semi-continuity of these attractors under the Sobolev norm when a family of <inline-formula><tex-math id="M1">\begin{document}$ (n+1) $\end{document}</tex-math></inline-formula>-dimensional thin domains degenerates onto an <inline-formula><tex-math id="M2">\begin{document}$ n $\end{document}</tex-math></inline-formula>-dimensional domain.