Random exponential attractor for second order non-autonomous stochastic lattice dynamical systems with multiplicative white noise in weighted spaces

Advances in Difference Equations

Shengfan Zhou¹  Luyao Wu¹  Haijuan Su¹ 

[1] Department of Mathematics, Zhejiang Normal University;

关键词: Random exponential attractor;    Stochastic lattice system;    Multiplicative white noise;    Cocycle;    Weighted space of sequences;   

DOI  :  10.1186/s13662-019-1983-x

来源: DOAJ

【 摘 要 】

Abstract This paper is concerned with the random exponential attractor for second order non-autonomous stochastic lattice system with multiplicative white noise and unbounded nonlinearity. Firstly, we transfer the stochastic lattice system into a random lattice system without noise term whose solutions generate a continuous cocycle on a weighted space of infinite sequences. Then we present some sufficient conditions for the existence of a random exponential attractor for a continuous cocycle in the product weighted space of sequences, which improved the existing conditions. Finally, we prove the existence of a random exponential attractor for the considered system in weighted space of sequences.

【 授权许可】

Unknown