Global Attractor For The Cahn-Hilliard Equation With A Proliferation Term

This thesis is concerned with the existence of the global attractor of the Cahn-Hilliard equation with a proliferation term in Hk spaces.By means of the method in Reference[15],the result of existence of global attractor is obtained by applying the iteration procedure and regularity estimates.The thesis is divided into three chapters,and the specific content is as follows:In Chapter 1,the research background of Cahn-Hilliard equation and the existing research results are introduced.In addition,the well-posedness of the initial boundary value problem of Cahn-Hilliard equation with a proliferation term is given.In Chapter 2,the basic function spaces,definitions,theorems and inequalities necessary for the research are given.In Chapter 3,it is proved that the Cahn-Hilliard equation with a proliferation term has a global attractor in Hk space by using the iterative idea,the existence theorem of global attractor and the regularity estimation of linear semigroups.