Random exponential attractor for stochastic reaction-diffusion equation with multiplicative noise in R3

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Thou, Shengfan¹ 

[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China

关键词: Stochastic reaction diffusion equation;    Cocycle;    Random exponential attractor;    Fractal dimension;   

DOI  :  10.1016/j.jde.2017.07.013

来源: Elsevier

【 摘 要 】

In this paper, we first improve the existing conditions for the existence of a random exponential attractor for a continuous cocycle on a separable Banach space. Then we consider the existence of a random exponential attractor for stochastic non-autonomous reaction diffusion equation with multiplicative noise defined in R-3, which implies the existence of a random attractor with finite fractal dimension. The essential difficulty here is the continuity of the spectrum of the linear part of the equation, which can be overcome by the tail estimation of solutions of equation and carefully decomposing the solution into a sum of three parts, of whose, one part is finite-dimensional and other two parts are quickly decay in mean sense. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free