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A Conserved Phase-Field Model Based on Microconcentrations
Faculté des Sciences et Techniques, Université Marien Ngouabi, Brazzaville, Republic of the Congo
Institut Supérieur d’Architecture, Urbanisme, Batiment et Travaux Publics, Université Denis Sassou N’guesso, Kintele, Republic of the Congo
Laboratoire de Mécanique, Energétique et Ingégnerie, Ecole Nationale Supérieure Polytechnique, Université Marien Ngouabi, Brazzaville, Republic of the Congo
- 1 Faculté des Sciences et Techniques, Université Marien Ngouabi, Brazzaville, Republic of the Congo
- 2 Institut Supérieur d’Architecture, Urbanisme, Batiment et Travaux Publics, Université Denis Sassou N’guesso, Kintele, Republic of the Congo
- 3 Laboratoire de Mécanique, Energétique et Ingégnerie, Ecole Nationale Supérieure Polytechnique, Université Marien Ngouabi, Brazzaville, Republic of the Congo
Applied Mathematics·Volume 16 (2025)·Pages 275–291·Published 25 March 2025·DOI10.4236/am.2025.163014
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Abstract
In this article, we consider the conserved phase-field model based on microconcentrations. In particular, we prove the well-posedness to this model and then prove the convergence of the solutions to those of the classical conserved phase-field model as a small parameter goes to zero, on finite time intervals. We also prove the existence of global attractor and we finally give some numerical simulations.
KeywordsConserved Phase-Field ModelMicroconcentrationsNeumann Boundary ConditionsWell-PosednessPassage to the LimitGlobal AttractorNumerical Simulations
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