Asymptotic Behavior For A Class Of Stochastic Ginzburg-Landau Equations In Bochner Spaces

In this thesis,we study the asymptotic behavior of the stochastic GinzburgLandau equations driven by nonlinear noise.Firstly,we study the mean random dynamical systems generated by deterministic Ginzburg-Landau equations with random initial data.Secondly,the existence of weak pullback mean random attractors for the deterministic equation in Bochner space is proved.In this case,the periodicity of the weak pullback mean random attractors is also proved whenever the external forcing terms are periodic in time.Then,the well-posedness of the solution of stochastic Ginzburg-Landau equation is studied by variational method.Furthermore,based on the well-posedness of the solution,the corresponding mean random dynamical systems is given,and the existence of weak pullback mean random attractors of stochastic Ginzburg-Landau equations is proved.Finally,the existence of invariant measures for stochastic Ginzburg-Landau equations is established.This thesis is organized as follows:In Chapter 1,The research background of stochastic Ginzburg-Landau equations is introduced,and the main work of this thesis is briefly stated.In Chapter 2,The concepts and theorems of mean random attractors for mean random dynamical systems are given.In Chapter 3,The well-posedness of the solution of the deterministic Ginzburg-Landau equations with random initial data is studied,and the existence of the mean random attractors of the deterministic equations in the Bochner spaces is proved.In Chapter 4,The well-posedness of the solution of stochastic Ginzburg-Landau equations is given,and the existence of the weak pullback mean random attractors of the stochastic equations is considered.In Chapter 5,The existence of invariant measures of the stochastic Ginzburg-Landau equations is studied.In Chapter 6,The main results are summarized and some problems for future research are proposed.