# American Institute of Mathematical Sciences

doi: 10.3934/cpaa.2020242

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

 1 School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China 2 National Engineering Laboratory of Integrated Transportation, Big Data Application Technology, Chengdu 61756, China

* Corresponding author

Received  February 2020 Revised  July 2020 Published  September 2020

Fund Project: The first author is supported by the National Natural Science Foundation of China (grant No. 11701475, 1197130 and 11971394)

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.

Citation: Lin Shi, Xuemin Wang, Dingshi Li. Limiting behavior of non-autonomous stochastic reaction-diffusion equations with colored noise on unbounded thin domains. Communications on Pure & Applied Analysis, doi: 10.3934/cpaa.2020242
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