Published Paper

Inserted: 1 apr 2009
Last Updated: 25 jul 2011

Journal: J. Differential Equations
Volume: 251
Pages: 785-815
Year: 2011

Abstract:

In this work, we consider a general fully overdamped Frenkel-Kontorova model. This model describes the dynamics of a 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.

Keywords: particle systems, periodic homogenization, Hamilton-Jacobi equations, nonlinear diffusion

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