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

• Main Authors: Haijuan Su, Shengfan Zhou, Luyao Wu
• Format: Article
• Language: English
• Published: SpringerOpen 2019-01-01
• Series: Advances in Difference Equations
• Subjects: Random exponential attractor; Stochastic lattice system; Multiplicative white noise; Cocycle; Weighted space of sequences
• Online Access: http://link.springer.com/article/10.1186/s13662-019-1983-x

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.