Diffusion limit of the vlasov-poisson-fokker-planck system

Najoua El Ghani, Nader Masmoudi

Research output: Contribution to journalArticlepeer-review

Abstract

We study the diffusion limit of the Vlasov-Poisson-Fokker-Planck System. Here, we generalize the local in time results and the two dimensional results of Poupaud-Soler [F. Poupaud and J. Soler, Math. Models Methods Appl. Sci., 10(7), 1027-1045, 2000] and Goudon [T. Goudon, Math. Models Methods Appl. Sci., 15(5), 737-752, 2005] to the case of several space dimensions. Renormalization techniques, the method of moments and a velocity averaging lemma are used to prove the convergence of free energy solutions (renormalized solutions) to the Vlasov-Poisson-Fokker-Planck system towards a global weak solution of the Drift-Diffusion-Poisson model.

Original languageEnglish (US)
Pages (from-to)463-479
Number of pages17
JournalCommunications in Mathematical Sciences
Volume8
Issue number2
DOIs
StatePublished - Jun 2010

Keywords

  • Drift-Diffusion-Poisson model
  • Hydrodynamic limit
  • Moment method
  • Renormalized solutions
  • Velocity averaging lemma
  • Vlasov-Poisson-Fokker-Planck system

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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