Homogenization of fully overdamped Frenkel-Kontorova models

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:246

Article

Forcadel, N.^2,3,4  Imbert, C.¹  Monneau, R.² 

[1] Univ Paris 09, CNRS, CEREMADE, UMR 7534, F-75775 Paris 16, France

[2] Paris Est ENPC, CERMICS, F-77455 Marne La Vallee 2, France

[3] Ecole Polytech, CMAP INRIA Futurs, Projet Commands, F-91128 Palaiseau, France

[4] UMA, ENSTA, F-75739 Paris 15, France

关键词: Particle systems;    Periodic homogenization;    Frenkel-Kontorova models;    Hamilton-Jacobi equations;    Hull function;    Cumulative distribution function;    Slepcev formulation;   

DOI  :  10.1016/j.jde.2008.06.034

来源: Elsevier

【 摘 要 】

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. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

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