Asymptotic behavior of a model for order-disorder and phase separation

Article type: Research Article

Authors: Miranville, Alain^a | Saoud, Wafa^{a; *} | Talhouk, Raafat^b

Affiliations: [a] Laboratoire de Mathématiques et Applications, Université de Poitiers, UMR CNRS 7348 – SP2MI, Boulevard Marie et Pierre Curie – Téléport 2, F-86962 Chasseneuil Futuroscope Cedex, France. E-mails: [email protected], [email protected] | [b] Laboratoire de Mathématiques – EDST et Faculté des Sciences, Université Libanaise, Hadath, Liban. E-mail: [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: Our aim in this article is to study the long time behavior, in terms of finite-dimensional attractors, of a coupled Allen–Cahn/Cahn–Hilliard system. In particular, we prove the existence of an exponential attractor and, as a consequence, the existence of the global attractor with finite fractal dimension.

Keywords: Allen–Cahn/Cahn–Hilliard system, global attractor, exponential attractor, fractal dimension

DOI: 10.3233/ASY-171419

Journal: Asymptotic Analysis, vol. 103, no. 1-2, pp. 57-76, 2017