WONG-ZAKAI APPROXIMATIONS AND ATTRACTORS FOR STOCHASTIC WAVE EQUATIONS DRIVEN BY ADDITIVE NOISE

被引：9

作者：

Wang, Xiaohu ^{[1
]}

Li, Dingshi ^{[2
]}

Shen, Jun ^{[1
]}

机构：

[1] Sichuan Univ, Dept Math, Chengdu 610064, Sichuan, Peoples R China

[2] Southwest Jiaotong Univ, Sch Math, Chengdu 610031, Sichuan, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2021年 / 26卷 / 05期

关键词：

Wave equation; white noise; random attractor; upper semicontinuity; REACTION-DIFFUSION EQUATIONS; RANDOM DYNAMICAL-SYSTEMS; DIFFERENTIAL-EQUATIONS; SMOOTH APPROXIMATION; CHAOTIC BEHAVIOR; MANIFOLDS; CONVERGENCE;

D O I：

10.3934/dcdsb.2020207

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the Wong-Zakai approximations given by a stationary process via Euler approximation of Brownian motion and the associated long term behavior of the stochastic wave equation driven by an additive white noise on unbounded domains. We first prove the existence and uniqueness of tempered pullback attractors for stochastic wave equation and its Wong-Zakai approximation. Then, we show that the attractor of the Wong-Zakai approximate equation converges to the one of the stochastic wave equation driven by additive noise as the correlation time of noise approaches zero.

引用

页码：2829 / 2855

页数：27

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