With The Progressive Nature Of The Nonlinear Terms Cahn-hilliard Equation

This paper studies the asymptotic behavior of solutions of a class of fourth order Cahn-Hilliard equations with a general nonlinear term: Where K(u)=-△u+f(u) with f(u) satisfying some suitable conditions, u=u(x,t) is the unknown function and Q is an open bounded subset of R"(n≤3) with sufficiently smooth boundary (?)Ω.Equation Q, as an important class of nonlinear diffusion equation, plays an extensive role in the filed of mathematics and physics. In this paper, we study the long time behavior of weak and strong solutions, and obtain the existence of the global weak and strong attractors of the equation.This thesis is mainly divided into two parts. In chapter three, we obtain the existence and uniqueness of global weak solution by Galerkin method and energy inequality. Then we prove the existence of the global attractor of the semigroup in L2(Ω) by the uniform compactness method. In chapter four, we obtain the existence and uniqueness of strong solution by using sectoral theory. Then we prove the existence of the global attractor of the semigroup in H2(Ω) by theω-limit compactness method.