Research On Pullback Attractors Of Two Kinds Of Infinite Dimensional Dynamical Systems

The problem of pullback attractors of two kinds of infinite dimensional dynamical systems is studied in this thesis. Firstly, the existence of pullback attractors for non-autonomous Cahn-Hilliard equation in the space of2 L is explored, Then the existence of pullback attractors for the viscous Cahn-Hilliard equation is disscussed.Finaly,we prove the existence of pullback attractors of nonautonomous reaction-diffusion equation.This thesis consists of four portions as following:In the first part, we introduce the summarization of dynamical systems, autonomous systems, non-autonomous systems and the pullback attractors, and also introduce the background of them and briefly show the development and research for them.In the second part, some preliminary results are presented. They include some basic inequalities and common spaces, then the characters and the theorems of pullback attractors are introduced.In the third part, the dynamic problem of non-autonomous Cahn-Hilliard equation is studied. Above all, the existence of pullback attractors for it is proved. The existence of pullback absorbing set was given, then it is proved the existence of pullback D-attractors for the class of the non-autonomous Cahn-Hilliard equation by the pullback condition(C)in the space of2 L. At the same time, the pullback attractors of the viscous Cahn-Hilliard equation is proved.In the end of this article, the existence of pullback attractors of the non-autonomous reaction-diffusion equation was investigated, with the skills of inequality and the pullback condition(C), it is proved the existence of pullback attractors for the class of thenon-autonomous reaction-diffusion equation in the space of2 L.