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| HAL: hal-00266994, version 2 |
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| Journal of Differential Equations 246 (2009) pp 1057--1097 |
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| Available versions: | v1 (2008-03-26) | v2 (2008-03-31) |
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| Homogenization of fully overdamped Frenkel-Kontorova models |
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| Nicolas Forcadel 1, 2Cyril Imbert 3 |
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| (2009) |
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| In this paper, we consider the fully overdamped Frenkel-Kontorova model. This is an infinite system of coupled first order ODEs. Each ODE represents the microscopic evolution of one particle interacting with its neighbors and submitted to a fixed periodic potential. After a proper rescaling, a macroscopic model describing the evolution of densities of particles is obtained. We get this homogenization result for a general class of Frenkel-Kontorova models. The proof is based on the construction of suitable hull functions in the framework of viscosity solutions. |
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| 1: | 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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| 2: | Commands (INRIA Futurs) |
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INRIA – CNRS : UMR7641 |
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| 3: | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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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 – cumulative distribution function – Slepcev formulation. |
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| hal-00266994, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00266994 | |
| oai:hal.archives-ouvertes.fr:hal-00266994 | |
| From: Nicolas Forcadel | |
| Submitted on: Monday, 31 March 2008 09:22:54 | |
| Updated on: Wednesday, 11 February 2009 13:53:06 | |
