Diffusion as a singular homogenization of the Frenkel-Kontorova model

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:251

Article

Alibaud, N.^2,3  Briani, A.^1,4  Monneaue, R.⁵ 

[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

关键词: Particle systems;    Periodic homogenization;    Frenkel-Kontorova models;    Hamilton-Jacobi equations;    Nonlinear diffusion;   

DOI  :  10.1016/j.jde.2011.05.020

来源: Elsevier

【 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.

【 授权许可】

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