The Solvability Of Some Variant Equations Of Cahn-Hilliard Equation

In this thesis,we study the solvability of Cahn-Hilliard-Oono equation and vis-cous Cahn-Hilliard equation.The existence of solutions is proved by using the sectorial opera-tor theory and the existence theorem of the solution of abstract Cauchy problems.The full text is divided into three chapters:In Chapter 1,to introduce the background and current status of the research,and some basic definitions,theorems and lemmas needed for this thesis.In Chapter 2,the existence of solutions for Cahn-Hilliard-Oono equation is studied.First-ly,the existence of local solutions of Cahn-Hilliard-Oono equation is obtained by using the sectorial operator theory and the existence theorem of local solutions of abstract Cauchy prob-lem.Secondly,the existence of global solutions of Cahn-Hilliard-Oono equation is obtained by using the existence theorem of global solutions.Finally,the H2 norm estimate of the solution of the generalized equation is obtained.In Chapter 3,the solvability of viscous Cahn-Hilliard equation is studied.By constructing sectorial operators and using the existence theorem of the solution of abstract Cauchy prob-lem,the existence of local solutions and global solutions of viscous Cahn-Hilliard equation are proved.