Dynamics of a conserved phase-field system

Abstract

Recently, in Bonfoh [Ann. Mat. Pura Appl. 2011;190:105–144], we investigated the dynamics of a nonconserved phase-field system whose singular limit is the viscous Cahn–Hilliard equation. More precisely, we proved the existence of the global attractor, exponential attractors, and inertial manifolds and we showed their continuity with respect to a singular perturbation parameter. In the present paper, we extend most of these results to a conserved phase-field system whose singular limit is the nonviscous Cahn–Hilliard equation. These equations describe phase transition processes. Here, we give a direct proof of the existence of inertial manifolds that differs from our previous method that was based on introducing a change of variables and an auxiliary problem.