Global Attractors For Several Types Of Higher Order Diffusion Equations

The nonlinear diffusion equation studied in this paper belongs to the category of time-dependent partial differential equation,and was originally proposed in the study of natural diffusion phenomena.So far,nonlinear diffusion equations have been widely used in the fields of permeation research,phase transfer theory,biomathematics,microbial science,and mathematical model construction in human sociological research.In the research process,due to the complexity of some variables,the exact solution of most nonlinear diffusion equations is difficult to find,so in order to study the behavior of the solution,we usually consider the continuous asymptotic behavior of the solution,that is,the solution when the time t?? to conduct research on the behaviors and gradually introduce the overall attractor.This paper mainly considers the continuous behavior of the solutions of three generalized high-order nonlinear Cahn-Hilliard equations,and studies the existence of its overall attractor.The main work is as follows:In chapter 2,considering the continuous model of the natural formation of the angle surface in the crystal growth process,and study the existence of the global attractor for the initial boundary value problem of a class of fourth-order convective Cahn-Hilliard equation.We prove that the initial boundary value problem of the equation has the global attractor in space H4(?)when the initial value is u0?H1(?).In chapter 3,we study the initial boundary value problem of a class of sixth-order convection Cahn-Hilliard equations used to describe the slope change of crystal surface growth.Using a series of prior estimates and Temam theory,we proved that when the initial valueu0 ? H2(0,1),the equation has an overall attractor in space H6(0,1).In Chapter 4,we study the initial boundary value problem of a class of six-order Cahn-Hilliard equations with Willmore regularization in a three-dimensional smooth bounded region,and proved that when the initial values ?0?H2(?),the equation has an overall attractor in space H6(?).