The Research Of Time Periodic Solution For The Cahn-Hilliard Type Equation

In this thesis, we will use the energy method and Leray-Schauder’s fixed pointtheorem to study the periodic solutions and classical solution for three types ofCahn-Hilliard equation.This thesis consists of four parts,In the first part,we introduce the development of Cahn-Hilliard type equation,definition and two important lemmas appearing in the thesis.In the second part, we study the periodic solutions and classical solution ofviscous Cahn-Hilliard equation with varying mobility. We prove the existence of timeperiodic solutions and the existence and uniqueness of classical solution, theninvestigate the asymptotic estimates and asymptotic behavior of solutions.In the third part, we investigate the periodic solution and classical solution ofconvective Cahn-Hilliard equation with constant mobility. We prove the existenceand uniqueness of classical solutions and time periodic solutions, then study theasymptotic estimates of solutions of the initial boundary value problem and theattraction of nontrivial periodic solutions.In the forth part, we study the periodic solutions and classical solution ofconvective Cahn-Hilliard equation with varying mobility. We prove the existence oftime periodic solutions and the existence and uniqueness of classical solution, theninvestigate the asymptotic estimates of solutions of the initial boundary valueproblem.