On the Cahn-Hilliard equation in H-1(R-N)

Abstract

In this paper we exhibit the dissipative mechanism of the Cahn-Hilliard equation in H-1 (R-N). We show a weak form of dissipativity by showing that each individual solution is attracted, in some sense, by the set of equilibria. We also indicate that strong dissipativity, that is, asymptotic compactness in H-1 (R-N), cannot be in general expected. Then we consider two types of perturbations: a nonlinear perturbation and a small linear perturbation. In both cases we show that, for the resulting equations, the dissipative mechanism becomes strong enough to obtain the existence of a compact global attractor.