 |
|
|
|
| HAL : hal-00243982, version 1 |
| arXiv : 0802.0931 |
| Fiche détaillée |  Récupérer au format |
|
|
| International Conference for the 25th Anniversary of Viscosity Solutions, Tokyo : Japan (2007) |
|
|
|
|
| WEAK SOLUTIONS FOR DISLOCATION TYPE EQUATIONS |
|
|
| Olivier Ley 1, 2 |
|
|
| (2008) |
|
|
|
| We describe recent results obtained by G. Barles, P. Cardaliaguet, R. Monneau and the author recently. They are concerned with nonlocal Eikonal equations arising in the study of the dynamics of dislocation lines in crystals. These equations are nonlocal but also non monotone. We use a notion of weak solution to provide solutions for all time. Then, we discuss the link between these weak solutions and the classical viscosity solutions, and state some uniqueness results in particular cases. A counter-example to uniqueness is given. |
|
|
|
|
|
|
|
|
|
|
|
| 1 : | Laboratoire de Mathématiques et Physique Théorique (LMPT) |
|
|
|
CNRS : UMR6083 – Université François Rabelais - Tours |
|
|
| 2 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
|
|
|
CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – INSA Rennes – Université Rennes II |
|
|
|
|
|
|
|
|
|
| Domaine | : | Mathématiques/Equations aux dérivées partielles |
|
|
| Nonlocal Hamilton-Jacobi Equations – dislocation dynamics – level-set approach – lower-bound gradient estimate – viscosity solutions – $L^1$-dependence in time. |
|
|
|
| Liste des fichiers attachés à ce document : | ||||||||||
|
||||||||||
|
|
|
| hal-00243982, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00243982 | |
| oai:hal.archives-ouvertes.fr:hal-00243982 | |
| Contributeur : Olivier Ley | |
| Soumis le : Jeudi 7 Février 2008, 10:35:17 | |
| Dernière modification le : Vendredi 19 Février 2010, 15:51:35 | |
