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| HAL: hal-00264757, version 1 |
| arXiv: 0803.2480 |
| DOI: 10.1016/j.jfa.2009.04.014 |
| Detailed view |  Export this paper |
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| Journal of Functional Analysis 257, 5 (2009) 1261-1287 |
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| Uniqueness Results for Nonlocal Hamilton-Jacobi Equations |
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| Guy Barles 1Pierre Cardaliaguet 2 |
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| (2009) |
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| We are interested in nonlocal Eikonal Equations describing the evolution of interfaces moving with a nonlocal, non monotone velocity. For these equations, only the existence of global-in-time weak solutions is available in some particular cases. In this paper, we propose a new approach for proving uniqueness of the solution when the front is expanding. This approach simplifies and extends existing results for dislocation dynamics. It also provides the first uniqueness result for a Fitzhugh-Nagumo system. The key ingredients are some new perimeter estimates for the evolving fronts as well as some uniform interior cone property for these fronts. |
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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 de Brest (LM) |
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CNRS : UMR6205 – Université de Bretagne Occidentale [UBO] – Institut Supérieur des Sciences et Technologies de Brest (ISSTB) |
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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 – 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 – Fitzhugh-Nagumo system – 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-00264757, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00264757 | |
| oai:hal.archives-ouvertes.fr:hal-00264757 | |
| From: Guy Barles | |
| Submitted on: Monday, 17 March 2008 17:26:58 | |
| Updated on: Tuesday, 23 March 2010 14:05:06 | |
