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

共 50 条

[31] Classification of initial energy in a pseudo-parabolic equation with variable exponents
Fengjie Li
Jiaqi Liu
Bingchen Liu
Analysis and Mathematical Physics, 2021, 11
[32] Weak pullback mean random attractors for the stochastic convective Brinkman-Forchheimer equations and locally monotone stochastic partial differential equations
Kinra, K.
Mohan, M. T.
INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2022, 25 (01)
[33] WEAK PULLBACK MEAN RANDOM ATTRACTORS FOR NON-AUTONOMOUS p-LAPLACIAN EQUATIONS
Gu, Anhui
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2021, 26 (07): : 3863 - 3878
[34] Properties of Weak Solutions for a Pseudoparabolic Equation with Logarithmic Nonlinearity of Variable Exponents
Pan, Rongting
Gao, Yunzhu
Meng, Qiu
JOURNAL OF MATHEMATICS, 2023, 2023
[35] Weak mean attractors and invariant measures for stochastic Schrodinger delay lattice systems
Chen, Zhang
Wang, Bixiang
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2023, 35 (04) : 3201 - 3240
[36] Blow-up phenomena for a pseudo-parabolic equation with variable exponents
Di, Huafei
Shang, Yadong
Peng, Xiaoming
APPLIED MATHEMATICS LETTERS, 2017, 64 : 67 - 73
[37] Convergence of bi-spatial pullback random attractors and stochastic Liouville type equations for nonautonomous stochastic p-Laplacian lattice system
Wang, Jintao
Peng, Qinghai
Li, Chunqiu
JOURNAL OF MATHEMATICAL PHYSICS, 2024, 65 (12)
[38] Random periodic paths of stochastic periodic semi-flows through random attractors, synchronizations and Lyapunov exponents
Feng, Chunrong
Luo, Yan
COMPUTATIONAL & APPLIED MATHEMATICS, 2025, 44 (02)
[39] Random Attractors for Stochastic Ginzburg-Landau Equation on Unbounded Domains
Lu, Qiuying
Deng, Guifeng
Zhang, Weipeng
ABSTRACT AND APPLIED ANALYSIS, 2014,
[40] Existence of weak solutions to a certain homogeneous parabolic Neumann problem involving variable exponents and cross-diffusion
Gurusamy Arumugam
André H. Erhardt
Journal of Elliptic and Parabolic Equations, 2020, 6 : 685 - 709

← 1 2 3 4 5 →