Existence of Random Attractors for a Class of Second-Order Lattice Dynamical Systems with Brownian Motions. (3rd December 2014)

• Record Type: Journal Article
• Authors: Wang, Yamin; Huang, Ziqiao; Alsaadi, Fuad E.; Lauria, Stanislao; Liu, Yurong
• Other Names: Shen Bo Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2014(2014)
• Publication Date: 2014-12-03
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2014/970120
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : This paper is concerned with the random attractors for a class of second-order stochastic lattice dynamical systems. We first prove the uniqueness and existence of the solutions of second-order stochastic lattice dynamical systems in the space F = l λ 2 × l 2 . Then, by proving the asymptotic compactness of the random dynamical systems, we establish the existence of the global random attractor. The system under consideration is quite general, and many existing results can be regarded as the special case of our results.