ON THE COUPLED CAHN-HILLIARD EQUATIONS

This paper is concerned with a system of nonlinear partial differentia l equations, in short, the coupled Cahn-Hilliard equations, which cons ists of a fourth order quasilinear parabolic equation and a second ord er quasilinear parabolic equation. This system was recently derived by Penrose and Fife and also by Alt and Pawlow to describe the nonisothe rmal phase separation of a two-component system. The global existence and uniqueness of classical solutions is proved. The results about the asymptotic behavior, as time goes to infinity, of solution and about the existence and multiplicity of solutions to the corresponding stati onary problem, which is a nonlinear boundary value problem involving n onlocal term and constraints, are also obtained.