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| HAL: hal-00372407, version 1 |
| DOI: 10.1016/j.jde.2011.05.020 |
| Detailed view |  Export this paper |
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| Journal of Differential Equations 251, 4-5 (2011) 785-815 |
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| Diffusion as a singular homogenization of the Frenkel-Kontorova model |
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| Nathaël Alibaud 1Ariela Briani 2 |
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| (2011-08) |
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| In this work, we consider a general fully overdamped Frenkel-Kontorova model. This model describes the dynamics of a infinite chain of particles, moving in a periodic landscape. Our aim is to describe the macroscopic behavior of this system. We study a singular limit corresponding to a high density of particles moving in a vanishing periodic landscape. We identify the limit equation which is a nonlinear diffusion equation. Our homogenization approach is done in the framework of viscosity solutions. |
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| 1: | Laboratoire de Mathématiques (LM-Besançon) |
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CNRS : UMR6623 – Université de Franche-Comté |
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| 2: | Unité de Mathématiques Appliquées (UMA) |
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ENSTA ParisTech |
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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/Optimization and Control Mathematics/Analysis of PDEs |
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| particle systems – periodic homogenization – Frenkel-Kontorova models – Hamilton-Jacobi equations – nonlinear diffusion |
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| hal-00372407, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00372407 | |
| oai:hal.archives-ouvertes.fr:hal-00372407 | |
| From: Ariela Briani | |
| Submitted on: Wednesday, 1 April 2009 10:21:24 | |
| Updated on: Thursday, 22 December 2011 10:35:42 | |
