On the Cahn–Hilliard equation in H1(RN)

In this paper we exhibit the dissipative mechanism of the Cahn–Hilliard equation in H1(RN). 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 H1(RN), 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.