Abstract
In this paper, we consider the asymptotic behaviour of non-autonomous stochastic discrete complex Ginzburg-Landau equations with additive noise in weighted space . The existences of tempered random attractors for this equation in spaces and are proved respectively by tail estimates, which implies that the obtained -random attractor is compact and attracting in the topology of space. The main difficulty here is the lack of compactness on infinite lattices. To deal with this, we introduce a common embedding space of and and derive some tail-estimates of solutions.
Acknowledgments
The authors would like to thank the reviewers for their helpful comments. Joint research project of Laurent Mathematics Center of Sichuan Normal University and National-Local Joint Engineering Laboratory of System Credibility Automatic Verification.
Disclosure statement
No potential conflict of interest was reported by the author(s).