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Exponential attractors for a singularly perturbed Cahn-Hilliard system. (English) Zbl 1046.37047
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:
 37L30 Attractors and their dimensions, Lyapunov exponents 35B40 Asymptotic behavior of solutions of PDE 35B45 A priori estimates for solutions of PDE 35K55 Nonlinear parabolic equations 35K35 Higher order parabolic equations, boundary value problems