Asymptotic behavior of stochastic FitzHugh-Nagumo systems on unbounded thin domains

Abstract

This article is concerned with the asymptotic behavior of solutions of a class of non-autonomous stochastic Fitzhugh-Nagumo systems driven by multiplicative white noise on unbounded thin domains. The existence and uniqueness of tempered pullback random attractors are proved for the systems defined on (n+1)−dimensional unbounded narrow domains. We also establish the upper semicontinuity of these attractors when a family of (n+1)−dimensional unbounded thin domains collapses onto an n−dimensional unbounded domain. A cut-off method and a decomposition technique are employed to derive the pullback asymptotic compactness of solutions in order to overcome the difficulties caused by the non-compactness of Sobolev embeddings on unbounded domains as well as the lack of regularity of one component of the solutions.