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Diffusion as a singular homogenization of the Frenkel-Kontorova model

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.
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Nathaël Alibaud, Ariela Briani, Régis Monneau. Diffusion as a singular homogenization of the Frenkel-Kontorova model. Journal of Differential Equations, Elsevier, 2011, 251 (4-5), pp.785-815. ⟨10.1016/j.jde.2011.05.020⟩. ⟨hal-00372407⟩

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