Limiting behavior of non-autonomous stochastic reaction-diffusion equations on unbounded thin domains

Abstract

This article is concerned with the limiting behavior of dynamics of a class of nonautonomous stochastic partial differential equations driven by multiplicative white noise on unbounded thin domains. We first prove the existence of tempered pullback random attractors for the equations defined on (n + 1)-dimensional unbounded thin domains. Then, we show the upper semicontinuity of these attractors when the (n + 1)-dimensional unbounded thin domains collapse onto the n-dimensional space Rn. Here, the tail estimates are utilized to deal with the noncompactness of Sobolev embeddings on unbounded domains.