Properties Of Solutions Of A Class Of Fourth-order Parabolic Equations With Logarithmic Nonlinear Terms

In the past decade,with the development and progress of science and technology,the fourth-order parabolic equation has found important applications in physics,engineering,image processing and biomathematics.For example,the thin film equation derived from the diffusion of droplets on the solid surface is used to study the Cahn-Hilliard equation of phase transition.Therefore,the fourth-order parabolic equation has attracted the attention of many scholars,and has been extensively studied,including the existence,uniqueness,asymptotic and so on.In this paper,we study a class of fourth-order parabolic equations with logarithmic nonlinear terms.By using Sobolev embedding theorem,several important inequalities,potential well method and Galerkin method,this paper proves the properties of solutions for a class of fourth-order parabolic equations with logarithmic nonlinear terms under different initial energy conditions.The specific content of this paper is divided into following four chapters:In the first chapter,the research background of the fourth-order parabolic equations with logarithmic nonlinear terms and the research status at home and abroad are introduced,and the relevant concepts and some important inequalities in Sobolev pace are given.In chapter 2,the asymptotic several minimum burst time of the global weak solutions is proved to supplement the existing conclusions in reference Liao and Li.In Chapter 3,Galerkin method is used to study a class of fourth-order parabolic equations with logarithmic nonlinear terms.The existence of the global weak solution and the finite time blow-up of the blow-up solution are studied under the conditions of low initial capacity and critical initial energy respectively.In chapter 4,on the basis of chapter 3,we durther discuss the properties of solutions under the condition of high initial energy,and give the global existence of weak solutions and sufficient conditions for blasting.