Random Exponential Attractor For Second Order Nonautonomous Lattice Systems With Multiplicative White Noise

In this thesis,we consider the random exponential attractor for second order nonautonomous stochastic lattice system with multiplicative white noise.This thesis is divided into three chapters:In chapter 1,we first introduced the background and current situation of research,then we introduced the main work of this thesis.In chapter 2,we first gave some preliminaries of this thesis,then presented some sufficient conditions for the existence of a random exponential attractor for a continuous cocycle defined on a weighted space of infinite sequences.In chapter 3,we studied the existence of random exponential attractors for second order nonautonomous random lattice systems with multiplicative white noise in bounded and unbounded nonlinearities,respectively.Firstly,we transferred the second order stochastic lattice system with multiplicative white noise into a random lattice system without noise through the Ornstein-Uhlenbeck process,whose solutions generate a continuous cocycle on a weighted space of infinite sequences.Secondly,we estimated the bound and tail of solutions for the random system.Thirdly,we verified the Lipschitz continuity of the continuous cocycle and decomposed the difference between two solutions into a sum of two parts,and carefully estimated the bound of the norm of each part and the expectations of some random variables.Finally,we obtained the existence of random exponential attractors for the considered systems.