Homogenization of fully overdamped Frenkel-Kontorova models

Abstract : In this paper, we consider the fully overdamped Frenkel-Kontorova model. This is an infinite system of coupled first order ODEs. Each ODE represents the microscopic evolution of one particle interacting with its neighbors and submitted to a fixed periodic potential. After a proper rescaling, a macroscopic model describing the evolution of densities of particles is obtained. We get this homogenization result for a general class of Frenkel-Kontorova models. The proof is based on the construction of suitable hull functions in the framework of viscosity solutions.
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Nicolas Forcadel, Cyril Imbert, Régis Monneau. Homogenization of fully overdamped Frenkel-Kontorova models. Journal of Differential Equations, Elsevier, 2009, 246, pp 1057--1097. ⟨10.1016/j.jde.2008.06.034⟩. ⟨hal-00266994v2⟩

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