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| HAL : hal-00387818, version 3 |
| arXiv : 0906.1722 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (25-05-2009) | v2 (09-06-2009) | v3 (07-06-2011) |
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| Homogenization of accelerated Frenkel-Kontorova models with $n$ types of particles |
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| Nicolas Forcadel 1Cyril Imbert 1 |
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| (25/05/2009) |
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| We consider systems of ODEs that describe the dynamics of particles. Each particle satisfies a Newton law (including the acceleration term) where the force is created by the interactions with the other particles and with a periodic potential. The presence of a damping term allows the system to be monotone. Our study takes into account the fact that the particles can be different. After a proper hyperbolic rescaling, we show that the solutions to this system of ODEs converge to the solution of a macroscopic homogenized Hamilton-Jacobi equation. |
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| 1 : | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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| 2 : | 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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| CEREMADE |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Particle systems – periodic homogenization – Frenkel-Kontorova models – Hamilton-Jacobi equations – hull function |
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| hal-00387818, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00387818 | |
| oai:hal.archives-ouvertes.fr:hal-00387818 | |
| Contributeur : Cyril Imbert | |
| Soumis le : Lundi 6 Juin 2011, 22:09:54 | |
| Dernière modification le : Mardi 7 Juin 2011, 09:08:58 | |
