Diffusion and homogenization approximation for semiconductor boltzmann-poisson system

Nader Masmoudi, Mohamed Lazhar Tayeb

Research output: Contribution to journalArticle

Abstract

In this paper, the diffusion and homogenization approximation of the Boltzmann-Poisson system in the presence of a spatially oscillating electrostatic potential is studied. By analyzing the relative entropy, the uniform energy estimate for a well-prepared boundary data is proved. An averaging lemma and two-scale convergence techniques are used to prove rigorously the convergence of the scaled Boltzmann equation (coupled to Poisson) to a homogenized drift-diffusion-Poisson system.

Original languageEnglish (US)
Pages (from-to)65-84
Number of pages20
JournalJournal of Hyperbolic Differential Equations
Volume5
Issue number1
DOIs
StatePublished - Mar 2008

Fingerprint

Ludwig Boltzmann
Homogenization
Semiconductors
Siméon Denis Poisson
Averaging Lemmas
Approximation
Two-scale Convergence
Drift-diffusion
Uniform Estimates
Relative Entropy
Energy Estimates
Boltzmann Equation
Electrostatics

Keywords

  • Averaging lemma
  • Boltzmann-Poisson system
  • Diffusion approximation
  • Drift-diffusion equation
  • Homogenization
  • Renormalized solution
  • Semiconductors
  • Two-scale convergence

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis

Cite this

Diffusion and homogenization approximation for semiconductor boltzmann-poisson system. / Masmoudi, Nader; Tayeb, Mohamed Lazhar.

In: Journal of Hyperbolic Differential Equations, Vol. 5, No. 1, 03.2008, p. 65-84.

Research output: Contribution to journalArticle

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