Weak Attractors And Invariant Measures For A Class Of Stochastic Discrete Ginzburg-Landau Equations

This thesis studys the dynamics and invariant measures of complex Ginzburg-Landau equations driven by locally Lipschitz nonlinear noise in the entire integer.We first prove the existence and uniqueness of solutions.And mean random dynamical systems are also obtained by solution operators.Furthermore,the existence and uniqueness for weak pull-back random attractors in(?)~2are established by the uniform estimates of solutions.Finally,the existence of invariant measures is proved in(?)~2.The approach of uniform estimates on the tails of the solutions is used for obtaining the tightness of a family of probability distributions of solutions.This thesis is organized as follows:In Chapter 1,the research background of stochastic discrete Ginzburg-Landau equations is introduced,and the main work of this thesis is stated briefly.In Chapter 2,some definitions and theorems of mean random dynamical systems and mean random attractors are presented.In Chapter 3,the existence and uniqueness of mean square solutions are proved.In Chapter 4,the existence and uniqueness of weak pullback mean random attractors are studied.In Chapter 5,the existence of invariant measures is considered.In Chapter 6,the main results of this thesis and some problems for future research are summarized.