Diffusion as a singular homogenization of the Frenkel-Kontorova model

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Abstract

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. © 2011 Elsevier Inc.

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Alibaud, N., Briani, A., & Monneau, R. (2011). Diffusion as a singular homogenization of the Frenkel-Kontorova model. Journal of Differential Equations, 251(4–5), 785–815. https://doi.org/10.1016/j.jde.2011.05.020

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