The singular limit dynamics of the phase-field equations

Abstract

We consider the phase-field equations subject to Dirichlet boundary conditions. We construct families of exponential attractors and inertial manifolds which are continuous at any parameter of perturbation \({\epsilon >0 }\) including the singular limit case \({\epsilon=0}\). Besides, the continuity at \({\epsilon=0}\) is obtained with respect to a metric independent of \({\epsilon}\). Continuity properties of the global attractors are also examined.