Homogenization of accelerated Frenkel-Kontorova models with $n$ types of particles
Forcadel, Nicolas; Imbert, Cyril; Monneau, Régis (2012), Homogenization of accelerated Frenkel-Kontorova models with $n$ types of particles, Transactions of the American Mathematical Society, 364, p. 6187-6227. http://dx.doi.org/10.1090/S0002-9947-2012-05650-9
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00387818/en/
Journal nameTransactions of the American Mathematical Society
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Abstract (EN)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.
Subjects / Keywordsparticle system; periodic homogenization; Frenkel-Kontorova models; Hamilton-Jacobi equations; hull function
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