Homogenization of fully overdamped Frenkel-Kontorova models
نویسندگان
چکیده
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. AMS Classification: 35B27, 35F20, 45K05, 47G20, 49L25, 35B10.
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