The Well-Posedness Of Solution And Existence Of Global Attractor For Darcy-Cahn-Hilliard System

In this thesis,we study the Darcy-Cahn-Hilliard system which is the Cahn-Hilliard eqution coupled with the Darcy equation.Firstly,we use Galerkin method,prior estimates,Dominated Convergence Theorem and Aubin-Lions Lemma to obtain the existence of the weak solution.At the same time,we prove the uniqueness of the solution on the premise that the solution satisfies the proper regularity.Then we use Gronwall inequality to get the asymptotic estimates in L~2(?) and H~1(?)so that we prove the existence of the global attractor.