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.