Wong-Zakai approximations and attractors for stochastic wave equations driven by additive noise
type: Item
instance of: scholarly article
title: Wong-Zakai approximations and attractors for stochastic wave equations driven by additive noise
zbMATH Open document ID: 1472.60106
author: Xiaohu Wang
author: Dingshi Li
author: Jun Shen
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2021-06-17T00:00:00Z
review text: The authors investigate the asymptotic behavior of the solutions of the stochastic wave equation driven by an additive white noise on unbounded domains and its Wong-Zakai approximation. The main idea of Wong-Zakai approximation is to use deterministic differential equations to approximate the solutions of the stochastic differential equations. In the article, Brownian motion is approximated using the Euler approximation. The authors prove the existence and uniqueness of tempered pullback attractors for stochastic wave equation and its Wong-Zakai approximation. Then, they 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.
reviewed by: Pavel Stoynov
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B41
Mathematics Subject Classification ID: 60H40
Mathematics Subject Classification ID: 35L05
zbMATH DE Number: 7360488
zbMATH Keywords: stochastic wave equation
zbMATH Keywords: white noise
zbMATH Keywords: random attractor
zbMATH Keywords: upper semicontinuity
zbMATH Keywords: Wong-Zakai approximation
zbMATH Keywords: Brownian motion
zbMATH Keywords: Euler approximation
MaRDI profile type: Publication
full work available at URL: dcdsb.2020207
OpenAlex ID: W3038809926
Wikidata QID: Q114022660
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DOI: 10.3934/DCDSB.2020207
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