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

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. © 2010 International Press.