Wong-Zakai approximations and attractors for stochastic reaction-diffusion equations on unbounded domains

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

Wang, Xiaohu¹  Lu, Kening²  Wang, Bixiang³ 

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

[2] Brigham Young Univ, Dept Math, Provo, UT 84602 USA

[3] New Mexico Inst Min & Technol, Dept Math, Socorro, NM 87801 USA

关键词: Wong-Zakai approximation;    Reaction diffusion equation;    White noise;    Random dynamical systems;    Random attractor;    Upper semicontinuity;   

DOI  :  10.1016/j.jde.2017.09.006

来源: Elsevier

【 摘 要 】

In this paper, we study the Wong-Zakai approximations given by a stationary process via the Wiener shift and their associated long term behavior of the stochastic reaction diffusion equation driven by a white noise. We first prove the existence and uniqueness of tempered pullback attractors for the Wong-Zakai approximations of stochastic reaction diffusion equation. Then, we show that the attractors of Wong-Zakai approximations converges to the attractor of the stochastic reaction diffusion equation for both additive and multiplicative noise. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free