A random attractor for a stochastic second order lattice system with random coupled coefficients

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:395

Article

Zhou, Shengfan¹  Wei, Lu² 

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

[2] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

关键词: Random attractor;    Stochastic second order lattice system;    Random coupled coefficients;    Multiplicative white noise;    Weighted space of infinite sequences;    Upper semicontinuity;    Additive white noise;   

DOI  :  10.1016/j.jmaa.2012.04.080

来源: Elsevier

【 摘 要 】

In this paper, we mainly focus on the asymptotic behavior of solutions to the second-order stochastic lattice equations with random coupled coefficients and multiplicative white noises in weighted spaces of infinite sequences. We first transfer stochastic lattice equations into random lattice equations and prove the existence and uniqueness of solutions which generate a random dynamical system. Second we consider the existence of a tempered random bounded absorbing set and a random attractor for the system. Then we establish the upper semicontinuity of random attractors as the coefficient of the white noise term tends to zero. Finally we present the corresponding results for the system with additive white noises. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free