DIFFUSION LIMIT OF THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM

作者：El Ghani Najoua^*; Masmoudi Nader

来源：Communications in Mathematical Sciences, 2010, 8(2): 463-479.

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

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), 737-2005] 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 Vlassov-Poisson-Fokker-Planck system towards a global weak solution of the Drift-Diffusion-Poisson model.

• 出版日期2010-6