Communications in Mathematical Sciences

Volume 8 (2010)

Number 2

Special Issue on the Occasion of Andrew Majda’s Sixtieth Birthday: Part II

Diffusion limit of the Vlasov-Poisson-Fokker-Planck system

Pages: 463 – 479

DOI: http://dx.doi.org/10.4310/CMS.2010.v8.n2.a9

Authors

Najoua El Ghani

Nader Masmoudi

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 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.

Keywords

Hydrodynamic limit; Vlasov-Poisson-Fokker-Planck system; Drift-Diffusion-Poisson model; moment method; velocity averaging lemma; renormalized solutions

2010 Mathematics Subject Classification

35B25, 35Q99, 45K05

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