(L2, H1)-Random Attractors for Stochastic Reaction-Diffusion Equation on Unbounded Domains
This article is part of Special Issue:
Gang Wang,
Yanbin Tang,
Gang Wang
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China hust.edu.cn
Search for more papers by this authorCorresponding Author
Yanbin Tang
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China hust.edu.cn
Search for more papers by this authorGang Wang,
Yanbin Tang,
Gang Wang
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China hust.edu.cn
Search for more papers by this authorCorresponding Author
Yanbin Tang
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China hust.edu.cn
Search for more papers by this authorAcademic Editor: Grzegorz Lukaszewicz
Abstract
We study the random dynamical system generated by a stochastic reaction-diffusion equation with additive noise on the whole space ℝn and prove the existence of an (L2, H1)-random attractor for such a random dynamical system. The nonlinearity f is supposed to satisfy the growth of arbitrary order p − 1 (p ≥ 2). The (L2, H1)-asymptotic compactness of the random dynamical system is obtained by using an extended version of the tail estimate method introduced by Wang (1999) and the cut-off technique.
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