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International Journal of Differential Equations
Volume 2011 (2011), Article ID 628459, 23 pages
http://dx.doi.org/10.1155/2011/628459
Research Article

Asymptotic Behavior of Stochastic Partly Dissipative Lattice Systems in Weighted Spaces

Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, USA

Received 22 June 2011; Accepted 3 September 2011

Academic Editor: I. Chueshov

Copyright © 2011 Xiaoying Han. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study stochastic partly dissipative lattice systems with random coupled coefficients and multiplicative/additive white noise in a weighted space of infinite sequences. We first show that these stochastic partly dissipative lattice differential equations generate a random dynamical system. We then establish the existence of a tempered random bounded absorbing set and a global compact random attractor for the associated random dynamical system.