Inserted: 1 apr 2009
Last Updated: 25 jul 2011
Journal: J. Differential Equations
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