Wong-Zakai Approximations And Asymptotic Behavior Of Stochastic Ginzburg-Landau Equations

This thesis deals with the Wong-Zakai approximations given by a stationary process via the Wiener shift and asymptotic behavior of stochastic Ginzburg-Landau equations with nonlinear noise.We first study the well-posedness for the stochastic Ginzburg-Landau equations on bounded domains.Then,we show that the approximate equation has a pullback random attractor under much weaker conditions than the original stochastic equation.Next,when the stochastic Ginzburg-Landau equations are driven by multiplicative noise,we establish the convergence of the solution of the Wong-Zakai approximate equation and the upper semi-continuity of the random attractors of the approximate stochastic system as ? 0.Finally,we discuss the asymptotic behavior of the stochastic Ginzburg-Landau equations on unbounded domains,and prove its asymptotic compactness by the tail estimates method,and the existence of random attractors of stochastic Ginzburg-Landau equations is obtained.This thesis is organized as follows:In Chapter 1,we introduce the research background of stochastic Ginzburg-Landau equations,and briefly describe the main work of this thesis.In Chapter 2,we present some preliminary definitions and theories that will be used in this thesis.In Chapter 3,we consider the Wong-Zakai approximations and asymptotic behavior of the stochastic Ginzburg-Landau equations on bounded domains.In Chapter 4,we discuss the stochastic Ginzburg-Landau equations on unbounded domains,then prove the existence of the random attractor and the upper semicontinuity of the stochastic Ginzburg-Landau equations driven by multiplicative noise.In Chapter 5,we summarize the main results and propose some problems for future research.