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December  2020, 19(12): 5367-5386. doi: 10.3934/cpaa.2020242

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

 School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China, 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, 2020, 19 (12) : 5367-5386. doi: 10.3934/cpaa.2020242
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