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.
Highlights
1 Introduction It is well known that the dynamics of a random dynamical system can be determined by the random attractor
The random exponential attractor contains the random attractor with finite fractal dimension, which implies that the dynamics of a random dynamical system can be described by finite independent parameters
Zhou in [3] established the existence of a random exponential attractor for a continuous cocycle on a separable Banach space and the first order stochastic lattice system driven by linear multiplicative white noise
Summary
It is well known that the dynamics of a random dynamical system can be determined by the random attractor. It is well known that the random variable |z(ω)| is tempered and there exists Ω0 ⊆ Ω with P(Ω0) = 1, such that for every ω ∈ Ω0, t → z(θtω) is continuous in t and lim |z(θtω)| = lim t 0 z(θsω)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
