Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 63, pp. 1-28.
Title: Robust exponential attractors for singularly perturbed
phase-field type equations
Authors: Alain Miranville (Lab. d'Applications des Math. - SP2MI, France)
Sergey Zelik (Lab. d'Applications des Math. - SP2MI, France)
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.