The Cahn-Hilliard Model for the Kinetics of Phase Separation

In this paper we consider the Cahn-Hilliard mathematical continuum model of spinodal decomposition (or phase separation) of a binary alloy. The phenomenological model is derived in section one. The existence theory for the Cahn-Hilliard equation is reviewed in section two. Various aspects and generalizations are surveyed in section three. A finite element approximation is studied in section four and, in particular, two fully discrete schemes are shown to possess Lyapunov functionals. Finally in section five some numerical simulations are described.