Electron. J. Diff. Eqns., Vol. 2002(2002), No. 63, pp. 1-28.
Robust exponential attractors for singularly perturbed
phase-field type equations
Alain Miranville & Sergey Zelik
Abstract:
In this article, we construct robust (i.e. lower and upper
semicontinuous) exponential attractors for singularly
perturbed phase-field type equations. Moreover, we obtain
estimates for the symmetric distance between these exponential
attractors and that of the limit Cahn-Hilliard equation
in terms of the perturbation parameter. We can note that the
continuity is obtained without time shifts as it is the case
in previous results.
Submitted April 18, 2002. Published July 4, 2002.
Math Subject Classifications: 35B40, 35B45.
Key Words: Phase-field equations, exponential attractors,
upper and lower semicontinuity.
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Alain Miranville
Laboratoire d'Applications des Mathematiques - SP2MI
Boulevard Marie et Pierre Curie - Teleport 2
86962 Chasseneuil Futuroscope Cedex - France
e-mail: miranv@mathlabo.univ-poitiers.fr
Sergey Zelik
Laboratoire d'Applications des Mathematiques - SP2MI
Boulevard Marie et Pierre Curie - Teleport 2
86962 Chasseneuil Futuroscope Cedex - France
e-mail: zelik@mathlabo.univ-poitiers.fr
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