Homogenization of accelerated Frenkel-Kontorova models with $n$ types of particles

Abstract : 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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Transactions of the American Mathematical Society, American Mathematical Society, 2012, 364, pp.6187-6227. 〈10.1090/S0002-9947-2012-05650-9〉
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https://hal.archives-ouvertes.fr/hal-00387818
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Dernière modification le : mercredi 23 janvier 2019 - 17:34:04
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Nicolas Forcadel, Cyril Imbert, Régis Monneau. Homogenization of accelerated Frenkel-Kontorova models with $n$ types of particles. Transactions of the American Mathematical Society, American Mathematical Society, 2012, 364, pp.6187-6227. 〈10.1090/S0002-9947-2012-05650-9〉. 〈hal-00387818v3〉

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