Asymptotic behavior of stochastic fractional power dissipative equations on Rn

被引：52

作者：

Lu, Hong ^{[1
]}

Bates, Peter W. ^{[2
]}

Xin, Jie ^{[3
]}

Zhang, Mingji ^{[4
]}

机构：

[1] China Univ Min & Technol, Coll Sci, Xuzhou 221116, Jiangsu, Peoples R China

[2] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

[3] Ludong Univ, Sch Math & Stat Sci, Yantai 100191, Shandong, Peoples R China

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

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2015年 / 128卷

关键词：

Stochastic equation; Fractional Laplacian; Asymptotic compactness; Random attractor; Pullback attractor; WELL-POSEDNESS; CAUCHY-PROBLEM; ATTRACTORS; BOUNDARY; KINETICS;

D O I：

10.1016/j.na.2015.06.033

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a reaction-fractional diffusion equation with additive noise on the entire space R-n with particular interest in the asymptotic behavior of solutions. We first transform the equation into a random equation whose solutions generate a random dynamical system. A priori estimates for solutions are derived when the nonlinearity satisfies certain growth conditions. Using estimates for far-field values of solutions and a cut-off technique, asymptotic compactness is proved. Thus, the existence of a random attractor in L-2(R-n) is established. (c) 2015 Elsevier Ltd. All rights reserved.

引用

页码：176 / 198

页数：23

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