Homogenization of fully overdamped Frenkel-Kontorova models

被引：31

作者：

Forcadel, N. ^{[2
,3
,4
]}

Imbert, C. ^{[1
]}

Monneau, R. ^{[2
]}

机构：

[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

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2009年 / 246卷 / 03期

关键词：

Particle systems; Periodic homogenization; Frenkel-Kontorova models; Hamilton-Jacobi equations; Hull function; Cumulative distribution function; Slepcev formulation; HAMILTON-JACOBI EQUATIONS; VISCOSITY SOLUTIONS; DEVILS STAIRCASE;

D O I：

10.1016/j.jde.2008.06.034

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：1057 / 1097

页数：41

共 21 条

[1]

[Anonymous], 1938, PHYS SOVIET

[2]

[Anonymous], FRENKEL KONTOROVA MO

[3] EXACT MODELS WITH A COMPLETE DEVILS STAIRCASE [J].