Long-time behavior of the higher-order anisotropic Caginalp phase-field systems based on the Cattaneo law

Article type: Research Article

Authors: Ntsokongo, Armel Judice^{a; *} | Tathy, Christian^b

Affiliations: [a] Faculté des Sciences et Techniques, Université Marien Ngouabi, B.P. 69 Brazzaville, Congo. E-mail: armel.ntsokongo@umng.cg | [b] Laboratoire de Mécanique, Énergétique et Ingénierie, École, Nationale Supérieure Polytechnique, Université Marien Ngouabi, B.P. 69 Brazzaville, Congo. E-mail: tathychristian@yahoo.fr

Correspondence: [*] Corresponding author. E-mail: armel.ntsokongo@umng.cg.

Abstract: The aim of this paper is to study higher-order Caginalp phase-field systems based on the Maxwell–Cattaneo law, instead of the classical Fourier law. More precisely, one obtains well-posedness results, as well as the existence of finite-dimensional attractors.

Keywords: Phase-field systems, higher-order systems, Anisotropy, Maxwell–Cattaneo law, well-posedness, long-time behavior, dissipativity, global attractor, exponential attractor

DOI: 10.3233/ASY-211695

Journal: Asymptotic Analysis, vol. 128, no. 1, pp. 1-30, 2022