Weak Solutions And Global Attractors Of A Sixth-order Cahn-Hilliard Equation

In this thesis,we study the existence and uniqueness of weak solutions of a sixth-order Cahn-Hilliard equation,as well as the regularity of its global attractor.The main results are divided into the following two parts.The first part of this thesis is devoted to the existence and uniqueness of weak solutions.First of all,we study weak solutions of the equation in H-1(?)space by using Galerkin method and energy estimates.Then,we study weak solutions in L2(?)space by applying the method of spacial sequences and the theory of T weakly continuous operator.Last but not least,from the variational structure of the equation,we obtain the existence and uniqueness of its solution in H2(?)space.The second part of this thesis is devoted to the regularity of the global attractor of this equation.First of all,by using energy method and compact operator theory,we obtain the result that the equation possesses a global attractor in both H-1(?)space and L2(?)space.Then,from a characteristic of gradient type equations that energy decreases with time,we obtain the existence of the global attractor of the equation in H2(?)space.Finally,by using an iteration procedure,regularity estimates for semigroups of linear operators and a theorem for the existence of global attractors,we prove that this equation possesses a global attractor in Hk(?)space for any k? 0.