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| HAL: hal-00243982, version 1 |
| arXiv: 0802.0931 |
| Detailed view |  Export this paper |
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| International Conference for the 25th Anniversary of Viscosity Solutions, Tokyo : Japon (2007) |
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| WEAK SOLUTIONS FOR DISLOCATION TYPE EQUATIONS |
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| Olivier Ley 1, 2 |
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| (2008) |
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| 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. |
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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 – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Subject | : | Mathematics/Analysis of PDEs |
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| Nonlocal Hamilton-Jacobi Equations – dislocation dynamics – level-set approach – lower-bound gradient estimate – viscosity solutions – $L^1$-dependence in time. |
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| hal-00243982, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00243982 | |
| oai:hal.archives-ouvertes.fr:hal-00243982 | |
| From: Olivier Ley | |
| Submitted on: Thursday, 7 February 2008 10:35:17 | |
| Updated on: Friday, 19 February 2010 15:51:35 | |
