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June 2010 Diffusion limit of the Vlasov-Poisson-Fokker-Planck system
Najoua El Ghani, Nader Masmoudi
Commun. Math. Sci. 8(2): 463-479 (June 2010).


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 and of Goudon 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.


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Najoua El Ghani. Nader Masmoudi. "Diffusion limit of the Vlasov-Poisson-Fokker-Planck system." Commun. Math. Sci. 8 (2) 463 - 479, June 2010.


Published: June 2010
First available in Project Euclid: 25 May 2010

zbMATH: 1193.35228
MathSciNet: MR2664460

Primary: 35B25 , 35Q99 , 45K05

Keywords: Drift-Diffusion-Poisson model , Hydrodynamic limit , Moment method , renormalized solutions , velocity averaging lemma , Vlasov-Poisson-Fokker-Planck system

Rights: Copyright © 2010 International Press of Boston

Vol.8 • No. 2 • June 2010
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