Weak mean random attractors for nonautonomous stochastic parabolic equation with variable exponents

被引：2

作者：

Zhang, Jiangwei ^{[1
]}

Liu, Zhiming ^{[1
]}

Huang, Jianhua ^{[1
]}

机构：

[1] Natl Univ Def Technol, Coll Sci, Changsha 410073, Peoples R China

来源：

STOCHASTICS AND DYNAMICS | 2023年 / 23卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Weak mean random attractor; parabolic equation; variable exponent; nonlinear noise; variational method; P-LAPLACIAN EQUATIONS; UPPER SEMICONTINUITY; GLOBAL ATTRACTORS; FUNCTIONALS; EXISTENCE; DYNAMICS; GROWTH;

D O I：

10.1142/S0219493723500193

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, we consider the asymptotic behavior of solutions for nonautonomous stochastic parabolic equation with nonstandard growth condition driven by nonlinear multiplicative noise for the first time. First, by making use of variational method, we prove the existence and uniqueness of solutions, and then the mean random dynamical systems generated by stochastic parabolic equations with variable exponents are obtained. Finally, due to the influence of variable indexes (dependent on space variable), we show the existence of weak mean random attractors under suitable assumptions on the variable exponents and the diffusion term.

引用

页数：20

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