Diffusion as a singular homogenization of the Frenkel-Kontorova model

  • Alibaud N
  • Briani A
  • Monneau R
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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.

Author-supplied keywords

  • Frenkel-Kontorova models
  • Hamilton-Jacobi equations
  • Nonlinear diffusion
  • Particle systems
  • Periodic homogenization

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Authors

  • N. Alibaud

  • A. Briani

  • R. Monneau

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