Existence and continuity of uniform exponential attractors for a singular perturbation of a generalized Cahn–Hilliard equation

Abstract

We consider a singular perturbation of a generalized Cahn–Hilliard equation based on constitutive equations derived by M. Gurtin. Compared to the classical Cahn–Hilliard equation, these models take into account the work of internal microforces and the anisotropy of the material. We prove the existence of exponential attractors and their convergence with respect to the parameter of perturbation ε when it goes to zero.