Diffusion as a singular homogenization of the Frenkel-Kontorova model

被引：1

作者：

Alibaud, N. ^{[2
,3
]}

Briani, A. ^{[1
,4
]}

Monneaue, R. ^{[5
]}

机构：

[1] Univ Pisa, Dipartimento Matemat, I-56127 Pisa, Italy

[2] CNRS, Lab Math Besancon, UMR 6623, F-25030 Besancon, France

[3] Prince Songkla Univ, Fac Sci, Dept Math, Hat Yai 90112, Songkhla, Thailand

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

[5] Univ Paris Est, CERMICS, Ecole Ponts ParisTech, F-77455 Marne La Vallee 2, France

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2011年 / 251卷 / 4-5期

关键词：

Particle systems; Periodic homogenization; Frenkel-Kontorova models; Hamilton-Jacobi equations; Nonlinear diffusion; VISCOSITY SOLUTIONS; EQUATIONS; DYNAMICS;

D O I：

10.1016/j.jde.2011.05.020

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this work, we consider a general fully overdamped Frenkel-Kontorova model. This model describes the dynamics of an infinite chain of particles, moving in a periodic landscape. Our aim is to describe the macroscopic behavior of this system. We study a singular limit corresponding to a high density of particles moving in a vanishing periodic landscape. We identify the limit equation which is a nonlinear diffusion equation. Our homogenization approach is done in the framework of viscosity solutions. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：785 / 815

页数：31

共 13 条

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