Robust exponential attractors for singularly perturbed phase-field type equations

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.

Keywords

• Phase-field equations
• exponential attractors
• upper and lower semicontinuity.