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Research Article | Open Access

A conserved Caginalp phase-field system with two temperatures and a nonlinear coupling term based on heat conduction

Grace Noveli Belvy Louvila, Armel Judice Ntsokongo, Franck Davhys Reval Langa( ), Benjamin Mampassi
Faculté des Sciences et Technique, Université Marien Ngouabi, BP: 69, Brazzaville, Congo
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Abstract

Our aim in this paper is to study generalizations of the Caginalp phase-field system based on a thermomechanical theory involving two temperatures and a nonlinear coupling. In particular, we prove well-posedness results. More precisely, the existence and uniqueness of solutions, the existence of the global attractor and the existence of an exponential attractor.

Keywords

conserved Caginalp systemtwo temperatureswell-posednessdissipativityglobal attractorexponential attractor
CLC number: 35B41, 35B45, 35K55

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AIMS Mathematics
Volume 8 Issue 6,
June 2023
Pages 14485-14507
DOI: 10.3934/math.2023740

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Cite this article:
Louvila GNB, Ntsokongo AJ, Langa FDR, et al. A conserved Caginalp phase-field system with two temperatures and a nonlinear coupling term based on heat conduction. AIMS Mathematics, 2023, 8(6): 14485-14507. https://doi.org/10.3934/math.2023740

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Received: 31 January 2023
Revised: 20 March 2023
Accepted: 29 March 2023
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)