Homogenization and Hydrodynamic Limit for Fermi-Dirac Statistics Coupled to a Poisson Equation

Nader Masmoudi, Mohamed Lazhar Tayeb

Research output: Contribution to journalArticle

Abstract

This paper deals with the diffusion approximation of a Boltzmann-Poisson system modeling Fermi-Dirac statistics in the presence of an extra external oscillating electrostatic potential. Here we extend the analysis done in [19] to the case of a nonlinear collision operator. In addition to the averaging lemma and control from entropy dissipation used in [19], here we use two-scale Young measures and renormalization techniques to prove the convergence. This result rigorously justifies the formal analysis of [3].

Original languageEnglish (US)
Pages (from-to)1742-1773
Number of pages32
JournalCommunications on Pure and Applied Mathematics
Volume68
Issue number10
DOIs
StatePublished - Oct 1 2015

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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