On the Cahn-Hilliard equation in H1(RN)

[摘要] 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. (C) 2012 Elsevier Inc. All rights reserved.

[发布日期] 2012-12-15

[关键词] Cahn-Hilliard equation;Initial value problems for higher-order;parabolic equations;Semilinear parabolic equations;Asymptotic behavior of solutions;Attractors