The coupled Cahn–Hilliard/Allen–Cahn system with dynamic boundary conditions

Article type: Research Article

Authors: Makki, Ahmad^{a; b} | Miranville, Alain^a | Petcu, Madalina^{a; c; d; *}

Affiliations: [a] Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 7348 – SP2MI, Boulevard Marie et Pierre Curie – Téléport 2, F-86962 Chasseneuil Futuroscope Cedex, France. E-mails: ahmad.makki@math.univ-poitiers.fr, alain.miranville@math.univ-poitiers.fr, madalina.petcu@math.univ-poitiers.fr | [b] Lebanese American University, Departement of Computer Science and Mathematics, Beirut, Lebanon | [c] The Institute of Mathematics of the Romanian Academy, Bucharest, Romania | [d] The Institute of Statistics and Applied Mathematics of the Romanian Academy, Bucharest, Romania

Correspondence: [*] Corresponding author. E-mail: madalina.petcu@math.univ-poitiers.fr.

Abstract: In this article, we are interested in the study of the well-posedness as well as of the long time behavior, in terms of finite-dimensional attractors, of a coupled Allen–Cahn/Cahn–Hilliard system associated with dynamic boundary conditions. In particular, we prove the existence of the global attractor with finite fractal dimension.

Keywords: Cahn–Hilliard/Allen–Cahn equations, dynamic boundary conditions, well-posedness, global attractors, fractal dimension

DOI: 10.3233/ASY-211703

Journal: Asymptotic Analysis, vol. 128, no. 2, pp. 183-209, 2022