Well-posedness Of Solutions Of Cahn-hilliard Equation In R~3

In this thesis,the Cahn-Hilliard equation and Cahn-Hilliard-Oono equation,its generalized form,are studied in R~3.With the help of the theory of sectorial operator,the global well posedness of solutions are obtained.Afterwards,the dissipation of their semigroups are obtained by using the gradient system.In the first chapter,the research significance and main results of Cahn-Hilliard equation,as well as Cahn-Hilliard-Oono equation,are introduced.In the second chapter,we introduce the related function space,important inequalities,lemmas and theorems.In the third and fourth chapters,we study the Cauchy problem of two equations mentioned above.By verifying the local Lipschitz continuity of the nonlinear term of equations,the local solvability are proved.Afterwards,through a series of energy estimates,the global well posedness of equations are proved.Finally we show that,the semigroup of solutions are point dissipative.