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| HAL : hal-00458216, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Viscosity solutions of differential equations and related topics, Kyoto : Japan (2008) |
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| Nonlocal Hamilton-Jacobi equations related to dislocation dynamics and a FitzHugh-Nagumo system |
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| Olivier Ley 1, 2 |
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| (2009) |
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| We describe recent existence and uniqueness results obtained for nonlocal nonmonotone Eikonal equations modelling the evolution of interfaces. We focus on two model cases. The first one arises in dislocation dynamics and the second one comes from a FitzHugh-Nagumo system. The equation is nonlocal since, in both case, the velocity at a point of the boundary of the interface depends on the whole enclosed set via a convolution. In these models, the evolution is nonmonotone since we do not expect to have an inclusion principle. |
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| 1 : | Laboratoire de Mathématiques et Physique Théorique (LMPT) |
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CNRS : UMR6083 – Université François Rabelais - Tours |
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| 2 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – INSA Rennes – Université Rennes II |
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| Analyse numérique |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Nonlocal Hamilton-Jacobi Equations – dislocation dynamics – Fitzhugh-Nagumo system – nonlocal front propagation – level-set approach – lower-bound gradient estimate – viscosity solutions – eikonal equation – $L^1-$dependence in time. |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00458216, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00458216 | |
| oai:hal.archives-ouvertes.fr:hal-00458216 | |
| Contributeur : Olivier Ley | |
| Soumis le : Vendredi 19 Février 2010, 16:35:45 | |
| Dernière modification le : Mardi 23 Mars 2010, 14:02:22 | |
