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

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Cholewa, Jan W. and Rodríguez Bernal, Aníbal (2012) On the Cahn-Hilliard equation in H-1(R-N). Journal of Differential Equations, 253 (12). 3678 -3726. ISSN 0022-0396

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022039612003476


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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.


Item Type:Article
Uncontrolled Keywords:Cahn-Hilliard equation; Initial value problems for higher-order; parabolic equations; Semilinear parabolic equations; Asymptotic behavior of solutions; Attractors
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:17430
Deposited On:13 Dec 2012 10:14
Last Modified:12 Dec 2018 15:07

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