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| HAL : hal-00549828, version 2 |
| arXiv : 1201.3444 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (23-12-2010) | v2 (17-01-2012) |
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| On a phase field model for solid-liquid phase transitions |
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| Sylvie Benzoni-Gavage 1Laurent Chupin 2 |
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| (03/12/2010) |
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| A new phase field model is introduced, which can be viewed as nontrivial generalisation of what is known as the Caginalp model. It involves in particular nonlinear diffusion terms. By formal asymptotic analysis, it is shown that in the sharp interface limit it still yields a Stefan-like model with: 1) a (generalized) Gibbs-Thomson relation telling how much the interface temperature differs from the equilibrium temperature when the interface is moving or/and is curved with surface tension; 2) a jump condition for the heat flux, which turns out to depend on the latent heat and on the velocity of the interface with a new, nonlinear term compared to standard models. From the PDE analysis point of view, the initial-boundary value problem is proved to be locally well-posed in time (for smooth data). |
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| 1 : | Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées de Lyon |
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| 2 : | Laboratoire de Mathématiques |
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CNRS : UMR6620 – Université Blaise Pascal - Clermont-Ferrand II |
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| 3 : | CEA (DEN/DTP/SMTH) |
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CEA : DEN/DTP/SMTH |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Phase field – Caginalp model – Sharp interface – Nonlinear diffusion |
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| hal-00549828, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00549828 | |
| oai:hal.archives-ouvertes.fr:hal-00549828 | |
| Contributeur : Sylvie Benzoni-Gavage | |
| Soumis le : Lundi 16 Janvier 2012, 16:00:06 | |
| Dernière modification le : Mardi 17 Janvier 2012, 08:50:24 | |
