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Zbl 1046.37047
Efendiev, Messoud; Miranville, Alain; Zelik, Sergey
Exponential attractors for a singularly perturbed Cahn-Hilliard system. (English)
[J] Math. Nachr. 272, 11-31 (2004). ISSN 0025-584X; ISSN 1522-2616/e

Summary: Our aim here is to give a construction of exponential attractors that are continuous under perturbations of the underlying semigroup. We note that the continuity is obtained without time shifts as it was the case in previous studies. Moreover, we obtain an explicit estimate on the symmetric distance between the perturbed and unperturbed exponential attractors in terms of the perturbation parameter. As an application, we prove the continuity of exponential attractors for a viscous Cahn-Hilliard system to an exponential attractor for the limit Cahn-Hilliard system.

MSC 2000:: *37L30 Attractors and their dimensions
35B40 Asymptotic behavior of solutions of PDE
35B45 A priori estimates
35K55 Nonlinear parabolic equations
35K35 Higher order parabolic equations, boundary value problems

Keywords: Exponential attractors; continuity; viscous Cahn-Hilliard system; a priori estimates; existence and uniqueness of solutions; asymptotic behavior

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