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

Abstract

This article is concerned with the limiting behavior of dynamics of a class of non-autonomous stochastic partial differential equations driven by colored 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 $ \mathbb{R}^n $. Here, the tail estimates are utilized to deal with the non-compactness of Sobolev embeddings on unbounded domains.