Contents Online
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: https://dx.doi.org/10.4310/CMS.2010.v8.n2.a9
Authors
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
Published 1 January 2010