Diffusion limit of the Vlasov-Poisson-Fokker-Planck system. (English) Zbl 1193.35228

Summary: 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.


35Q83 Vlasov equations
35B40 Asymptotic behavior of solutions to PDEs
35B25 Singular perturbations in context of PDEs
45K05 Integro-partial differential equations
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