Study Of Attractors For The Reaction-diffusion Equation And Degenerate Parabolic Equation

In the paper,we study the convergence of attractors for fractional reaction-diffusion equation,retarded reaction-diffusion equation and retarded degenerate parabolic equation.Under the condition of uniform boundedness,the forward convergence and backward con-vergence for the pullback attractor towards global attractor were proved by using the con-vergence theorems.This article is divided into five chapters.In chapter 1,the physical background,research status and development of dynami-cal systems were described,some theoretical knowledge and main research contents were introduced.In chapter 2,the existing basic definitions and theorems were given.the forward con-vergence and backward convergence theorem were given under bounded conditions.In chapter 3,the convergence of the attractor for the fractional reaction-diffusion equa-tion were considered,the forward convergence and backward convergence of the attractor were proved by using the convergence theorems.In chapter 4,the convergence of the attractor for the retarded reaction-diffusion equation were studied,the condition of nonlinear term f was limited to prove the forward convergence and backward convergence for the pullback attractor towards global attractor.In chapter 5,the convergence of the attractor for the retarded degenerate parabolic equation were studied,and the forward convergence and backward convergence of the at-tractor for the equation were proved by using the convergence theorems under the limited conditions.