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oai:docta.ucm.es:20.500.14352/424392023-08-27T12:17:23Zcom_20.500.14352_14col_20.500.14352_15

Cholewa, Jan W. Rodríguez Bernal, Aníbal 2023-06-20T00:21:02Z 2023-06-20T00:21:02Z 2012-12 0022-0396 10.1016/j.jde.2012.08.033 https://hdl.handle.net/20.500.14352/42439 http://www.sciencedirect.com/science/article/pii/S0022039612003476 http://www.sciencedirect.com/ 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. eng restricted access On the Cahn-Hilliard equation in H-1(R-N) journal article