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| HAL : hal-00486802, version 1 |
| arXiv : 1005.5597 |
| DOI : 10.1007/s00208-011-0648-1 |
| Fiche détaillée |  Récupérer au format |
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| Mathematische Annalen 352, 2 (2012) 409-451 |
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| Short Time Uniqueness Results for Solutions of Nonlocal and Non-monotone Geometric Equations |
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| Guy Barles 1, 2Olivier Ley 1, 3 |
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| (2012) |
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| We describe a method to show short time uniqueness results for viscosity solutions of general nonlocal and non-monotone second-order geometric equations arising in front propagation problems. Our method is based on some lower gradient bounds for the solution. These estimates are crucial to obtain regularity properties of the front, which allow to deal with nonlocal terms in the equations. Applications to short time uniqueness results for the initial value problems for dislocation type equations, asymptotic equations of a FitzHugh-Nagumo type system and equations depending on the Lebesgue measure of the fronts are presented. |
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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 : | Fédération de recherche Denis Poisson (FRDP) |
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CNRS : FR2964 – Université d'Orléans – Université François Rabelais - Tours |
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| 3 : | 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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| 4 : | Department of Applied Mathematics |
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Hiroshima University |
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| Analyse numérique |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Nonlocal Hamilton-Jacobi Equations – Nonlocal Front Propagation – Short Time Uniqueness – Non-Fattening Condition – Lower Gradient Estimate – Dislocation Dynamics – Fitzhugh-Nagumo System – Viscosity Solution |
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| hal-00486802, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00486802 | |
| oai:hal.archives-ouvertes.fr:hal-00486802 | |
| Contributeur : Olivier Ley | |
| Soumis le : Mercredi 26 Mai 2010, 17:28:45 | |
| Dernière modification le : Jeudi 16 Février 2012, 16:25:50 | |
