\((L^2,H^1)\)-random attractors for stochastic reaction-diffusion equation on unbounded domains
type: Item
instance of: scholarly article
title: \((L^2,H^1)\)-random attractors for stochastic reaction-diffusion equation on unbounded domains
zbMATH Open document ID: 1343.37080
DOI: 10.1155/2013/279509
author: Gang Wang
author: Yanbin Tang
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: We study the random dynamical system generated by a stochastic reaction-diffusion equation with additive noise on the whole space \(\mathbb R^n\) and prove the existence of an \((L^2,H^1)\)-random attractor for such a random dynamical system. The nonlinearity \(f\) is supposed to satisfy the growth of arbitrary order \(p-1(p\geq 2)\). The \((L^2,H^1)\)-asymptotic compactness of the random dynamical system is obtained by using an extended version of the tail estimate method introduced by \textit{B. Wang} [Physica D 128, No. 1, 41--52 (1999; Zbl 0953.35022)] and the cut-off technique.
Mathematics Subject Classification ID: 37L30
Mathematics Subject Classification ID: 37L55
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35R60
zbMATH DE Number: 6306595
Wikidata QID: Q58915786
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/279509
OpenAlex ID: W1989728093
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description: scientific article; zbMATH DE number 6306595