Well-posedness and long time behavior of a perturbed Cahn–Hilliard system with regular potentials

Article type: Research Article

Authors: Israel, Haydi | Miranville, Alain^; | Petcu, Madalina^;

Affiliations: UMR 7348 CNRS, Laboratoire de Mathématiques et Applications, Université de Poitiers, Poitiers, France. E-mails: [email protected], {alain.miranville, madalina.petcu}@math.univ-poitiers.fr | Institute of Mathematics of the Romanian Academy, Bucharest, Romania

Note: [] Corresponding author: Alain Miranville, UMR 7348 CNRS, Laboratoire de Mathématiques et Applications, Université de Poitiers, SP2MI, Boulevard Marie et Pierre Curie, Téléport 2 BP30179, 86962 Futuroscope Chasseneuil Cedex, France. E-mail: [email protected]

Abstract: The aim of this paper is to study the well-posedness and long time behavior, in terms of finite-dimensional attractors, of a perturbed Cahn–Hilliard equation. This equation differs from the usual Cahn–Hilliard by the presence of the term ε(−Δu+f(u)). In particular, we prove the existence of a robust family of exponential attractors as ε goes to zero.

Keywords: Cahn–Hilliard equation, regular potential, global attractor, exponential attractor

DOI: 10.3233/ASY-131172

Journal: Asymptotic Analysis, vol. 84, no. 3-4, pp. 147-179, 2013