Bi-spatial random attractor for stochastic FitzHugh-Nagumo systems on unbounded thin domain

Abstract

A bi-spatial random attractor is obtained for the stochastic FitzHugh-Nagumo systems on unbounded thin domains when the initial space is $L^2\times L^2$ and the terminate space is $L^p\times L^2$. Furthermore, we establish the upper semi-continuity of attractors under the $p$-norm when a family of $(n+1)$-dimensional thin domains degenerates into a $n$-dimensional unbounded domain.