Limiting behavior of non-autonomous stochastic reaction-diffusion equations on thin domains
type: Item
instance of: scholarly article
title: Limiting behavior of non-autonomous stochastic reaction-diffusion equations on thin domains
zbMATH Open document ID: 1360.60125
author: Dingshi Li
author: Bixiang Wang
author: Xiaohu Wang
published in: Journal of Differential Equations
publication date: 2016-12-22T00:00:00Z
review text: The aim of the paper is to study the asymptotic behaviour of the stochastic reaction-diffusion equation \[ du^\varepsilon- \Delta u^\varepsilon dt=( F(t, x,u^\varepsilon ) + G(t,x))dt + u^\varepsilon\circ dW \] with boundary condition \(\frac{du^\varepsilon}{d\nu_\varepsilon}=0\) where \(t>\tau\) and \(W\) is a two-sided real-valued Wiener process. Here, \(F\) is a nonlinear function satisfying some growth conditions and boundedness of partial derivatives and \(G\) is a function in \(L^2_{\text{loc}}\). The set on which this equation is defined is an this smooth bounded domain \({\mathcal O}_\varepsilon\) in \(\mathbb R^{n+1}\). The authors investigate what happens to the family of cocycles for above equations as \(\varepsilon\to 0\) and consider the question ``does there exist a limiting cocycle?''
reviewed by: Ruhollah Jahanipur
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B41
Mathematics Subject Classification ID: 37L30
zbMATH DE Number: 6668253
zbMATH Keywords: thin domain
zbMATH Keywords: stochastic reaction-diffusion equation
zbMATH Keywords: pullback attractor
zbMATH Keywords: upper semicontinuity
MaRDI profile type: Publication
full work available at URL: j.jde.2016.10.024
OpenAlex ID: W2541199285
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DOI: 10.1016/J.JDE.2016.10.024
description: scientific article; zbMATH DE number 6668253