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

Lin Shi; Xuemin Wang; Dingshi Li

doi:10.3934/cpaa.2020242

Article Contents

2020, Volume 19, Issue 12: 5367-5386. Doi: 10.3934/cpaa.2020242

This issue Previous Article Approximations of stochastic 3D tamed Navier-Stokes equations Next Article A global existence result for two-dimensional semilinear strongly damped wave equation with mixed nonlinearity in an exterior domain

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
^* Corresponding author

Received: February 2020

Revised: July 2020

Early access: September 2020

Published: December 2020

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

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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.

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Mathematics Subject Classification: Primary: 35B40; Secondary: 35B41, 37L30.

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