Homogenization and Hydrodynamic Limit for Fermi‐Dirac Statistics Coupled to a Poisson Equation | Zendy

Masmoudi Nader | Zendy; Tayeb Mohamed Lazhar | Zendy

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

Author(s) -

Masmoudi Nader,

Tayeb Mohamed Lazhar

Publication year - 2015

Publication title -

communications on pure and applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.12

H-Index - 115

eISSN - 1097-0312

pISSN - 0010-3640

DOI - 10.1002/cpa.21593

Subject(s) - homogenization (climate) , mathematics , poisson distribution , limit (mathematics) , mathematical physics , mathematical analysis , statistical physics , statistics , physics , biodiversity , ecology , biology

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]. © 2015 Wiley Periodicals, Inc.

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