数学
独特性
索波列夫空间
紧凑空间
拉回
有色的
吸引子
拉普拉斯算子
数学分析
应用数学
纯数学
复合材料
材料科学
作者
Xuping Zhang,Mengjie Zhang
出处
期刊:Discrete and Continuous Dynamical Systems-series B
[American Institute of Mathematical Sciences]
日期:2023-01-01
卷期号:28 (9): 4968-4992
标识
DOI:10.3934/dcdsb.2023049
摘要
This paper deals with the asymptotic behavior of the solutions to a class of non-autonomous fractional stochastic $ p $-Laplacian equations with delay driven by nonlinear colored noise on the entire space $ \mathbb{R}^n $. We firstly considered the existence of a continuous non-autonomous random dynamical system for the equations as well as the uniform estimates of solutions with respect to the time delay. We then showed pullback asymptotical compactness of solutions as well as the existence and uniqueness of tempered random attractors by utilizing the Arzela-Ascoli theorem and the uniform tail-estimates of the solutions for large space variables when time is large enough to surmount the lack of compact Sobolev embeddings on unbounded domains.
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