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; Grace Noveli Belvy Louvila; Armel Judice Ntsokongo; Franck Davhys Reval Langa; Benjamin Mampassi

doi:10.3934/math.2023740

AIMS Mathematics

2023, Volume 8, Issue 6: 14485-14507. doi: 10.3934/math.2023740

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Research article

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

Faculté des Sciences et Technique, Université Marien Ngouabi, BP: 69, Brazzaville, Congo

Received: 31 January 2023 Revised: 20 March 2023 Accepted: 29 March 2023 Published: 19 April 2023
MSC : 35B41, 35B45, 35K55

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.
- conserved Caginalp system,
- two temperatures,
- well-posedness,
- dissipativity,
- global attractor,
- exponential attractor
Citation: Grace Noveli Belvy Louvila, Armel Judice Ntsokongo, Franck Davhys Reval Langa, Benjamin Mampassi. A conserved Caginalp phase-field system with two temperatures and a nonlinear coupling term based on heat conduction[J]. AIMS Mathematics, 2023, 8(6): 14485-14507. doi: 10.3934/math.2023740

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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.

References

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