Random attractor for stochastic second-order non-autonomous stochastic lattice equations with dispersive term. Issue 2 (1st February 2016)

• Record Type: Journal Article
• Authors: Xiang, Xiaolin; Zhou, Shengfan
• Is Part Of: Journal of difference equations and applications. Volume 22:Issue 2(2016)
• Page Start: 235
• Page End: 252
• Publication Date: 2016-02-01
• Subjects: random attractor -- stochastic second-order lattice system -- dispersive term -- space of infinite sequences -- upper semi-continuity -- additive white noise; 60H15 -- 34C35 -- 58F11 -- 58F15 -- 58F36; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2015.1080694
• Languages: English
• ISSNs: 1023-6198

Abstract

Abstract : In this paper, we consider the asymptotic behaviour of solutions to second-order non-autonomous stochastic lattice equations with dispersive term and additive white noises in the space of infinite sequences. We first transfer the stochastic lattice equations into random lattice equations, and prove the existence and uniqueness of solutions that generate a random dynamical system. Second, we prove the existence of a tempered random absorbing set and a random attractor for the system. Finally, we establish the upper semi-continuity of the random attractors as the coefficient of the white noise term tends to zero.