The Existence And Uniqueness Of Solutions To A Class Of Fourth-order Partial Differential Equtions Characterizing Crystal Film Growth

In this paper,we mainly consider the mathematical theory of the fourth-order nonlinear parabolic equation,which describes the growth process of crystal film.That is,we will use Galerkin method,Banach fixed point theorem and other tools to study the fourth-order linear non-linear parabolic equation and the existence and uniqueness of its static equation solution.This paper is divided into three chapters:In chapter 1,the background of the theory of crystal film growth process is introduced.In chapter 2,some preliminary knowledge used in this paper is presented.Then,the existence of static equation solutions is obtained by using Lax-Milgram theorem and Banach fixed point theorem respectively.In chapter 3,the existence and uniqueness of the solutions of the corresponding linear parabolic equation are obtained by using Galerkin method and energy method,and then the existence and uniqueness of the solutions of the nonlinear fourth-order parabolic equation are derived.