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| HAL: hal-00129352, version 1 |
| arXiv: math.AP/0702153 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2007-02-06) | v2 (2009-02-13) |
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| GENERAL RESULTS FOR DISLOCATION TYPE EQUATIONS |
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| Guy Barles 1Pierre Cardaliaguet 2 |
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| (2007-02-06) |
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| We are interested in nonlocal Eikonal Equations arising in the study of the dynamics of dislocations lines in crystals. For these nonlocal but also non monotone equations, only the existence and uniqueness of Lipschitz and local-in-time solutions were available in some particular cases. In this paper, we propose a definition of weak solutions for which we are able to prove the existence for all time. Then we discuss the uniqueness of such solutions in several situations, both in the monotone and non monotone case. |
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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: | Laboratoire de Mathématiques (LM-Brest) |
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CNRS : FRE2218 – Université de Bretagne Occidentale (UBO) |
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| 3: | Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS) |
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INRIA – Ecole des Ponts ParisTech |
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| Subject | : | Mathematics/Analysis of PDEs |
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| Nonlocal Hamilton-Jacobi Equations – dislocation dynamics – nonlocal front propagation – level-set approach – geometrical properties – lower-bound gradient estimate – viscosity solutions – eikonal equation – $L^1-$dependence in time. |
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| hal-00129352, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00129352 | |
| oai:hal.archives-ouvertes.fr:hal-00129352 | |
| From: Olivier Ley | |
| Submitted on: Tuesday, 6 February 2007 17:34:35 | |
| Updated on: Tuesday, 6 February 2007 18:00:48 | |
