LIMITING BEHAVIOR OF NON-AUTONOMOUS STOCHASTIC REACTION-DIFFUSION EQUATIONS WITH COLORED NOISE ON UNBOUNDED THIN DOMAINS

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 R-n. Here, the tail estimates are utilized to deal with the non-compactness of Sobolev embeddings on unbounded domains.