The Research On The Dynamics Behavior Of Ginzburg-Landau Equation

This paper mainly discussed the dynamic behavior of the Ginzburg-Landau equation.First of all,the (G'/G) method was used to solve Ginzburg-Landau equation;then with the help of pullback conditions(C),this paper discuss the existence of a pullback attractor for the generalized Ginzburg-Landau equation in the spaceL~2,and at the same time we prove the existence of the pullback attractor of the nonlinear Ginzburg-Landau equation in 3 dimension space,finally we discuss the existence of the pullback attractor of the complex the Ginzburg-Landau equation.This paper includes the following four parts:The first part introduces the development course of infinite dimensional dynamical system,Ginzburg-Landau equation and the concept of pullback attractor as well as the research background and research status at home and abroad;In the second part,we recall the basic concepts and theorems used in this paper.Such as some inequalities and Sobolev theorems,the abstract result of pullback attractor;The third part deal with the existence of solutions for the two-dimensional constant coefficient of nonlinear Ginzburg-Landau equation.The fourth part is concerned with the existence of the pullback attractor of the generalized Ginzburg-Landau equation,the method is: using the existence and uniqueness of the solution to prove the existence of pullback absorbing sets,and with the help of pullback conditions(C),we proves the existence of pullback D-attractors for Ginzburg-Landau equations in the spaceL~2.Using the same method,we continue to study the existence of the pullback attractor of the nonlinear Ginzburg-Landau equation in 3 dimension space.Finally,with the help of inequality,we discuss the existence of pullback attractor of the complex Ginzburg-Landau equation.