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| HAL: hal-00387818, version 3 |
| arXiv: 0906.1722 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2009-05-25) | v2 (2009-06-09) | v3 (2011-06-07) |
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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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| (2009-05-25) |
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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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| Subject | : | Mathematics/Analysis of PDEs |
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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 | |
| From: Cyril Imbert | |
| Submitted on: Monday, 6 June 2011 22:09:54 | |
| Updated on: Tuesday, 7 June 2011 09:08:58 | |
