索波列夫空间
紧凑空间
拉回
吸引子
限制
拉回吸引子
随机偏微分方程
反应扩散系统
数学分析
数学
纯数学
空格(标点符号)
偏微分方程
计算机科学
工程类
操作系统
机械工程
作者
Lin Shi,Xuemin Wang,Dingshi Li
出处
期刊:Communications on Pure and Applied Analysis
[American Institute of Mathematical Sciences]
日期:2020-01-01
卷期号:19 (12): 5367-5386
被引量:1
摘要
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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