Diffusion limit of a semiconductor Boltzmann-Poisson system

Nader Masmoudi, Mohamed Lazhar Tayeb

Research output: Contribution to journalArticlepeer-review

Abstract

The paper deals with the diffusion limit of the initial-boundary value problem for the multidimensional semiconductor Boltzmann-Poisson system. Here, we generalize the one-dimensional results obtained in [5] to the case of several dimensions using global renormalized solutions. The method of moments and a velocity averaging lemma are used to prove the convergence of the renormalized solutions to the semiconductor Boltzmann-Poisson system towards a global weak solution of the drift-diffusion-Poisson model.

Original languageEnglish (US)
Pages (from-to)1788-1807
Number of pages20
JournalSIAM Journal on Mathematical Analysis
Volume38
Issue number6
DOIs
StatePublished - 2007

Keywords

  • Drift-diffusion model
  • Entropy dissipation
  • Kinetic transport equations
  • Moment method
  • Renormalized solution
  • Semiconductor Boltzmann-Poisson system
  • Velocity averaging lemma

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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