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| HAL : hal-00021694, version 1 |
| arXiv : math.AP/0603570 |
| DOI : 10.1080/03605300500361446 |
| Fiche détaillée |  Récupérer au format |
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| Comm. Partial Differential Equations 31, 7-9 (2006) 1191-1208 |
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| NONLOCAL FIRST-ORDER HAMILTON-JACOBI EQUATIONS MODELLING DISLOCATIONS DYNAMICS |
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| Guy Barles 1Olivier Ley 1, 2 |
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| (2006) |
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| We study nonlocal first-order equations arising in the theory of dislocations. We prove the existence and uniqueness of the solutions of these equations in the case of positive and negative velocities, under suitable regularity assumptions on the initial data and the velocity. These results are based on new $L^1$-type estimates on the viscosity solutions of first-order Hamilton-Jacobi Equations appearing in the so-called ``level-sets approach''. Our work is inspired by and simplifies a recent work of Alvarez, Cardaliaguet and Monneau. |
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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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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Nonlocal Hamilton-Jacobi Equations – dislocation dynamics – nonlocal front propagation – level-set approach – $L^1$-estimates – geometrical properties – lower-bound gradient estimate – semiconvexity – viscosity solutions. |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00021694, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00021694 | |
| oai:hal.archives-ouvertes.fr:hal-00021694 | |
| Contributeur : Olivier Ley | |
| Soumis le : Vendredi 24 Mars 2006, 09:33:14 | |
| Dernière modification le : Vendredi 19 Février 2010, 15:46:02 | |
