We are concerned with the analysis of the approximation by diffusion and homogenization of a Vlasov–Poisson–Fokker–Planck system. Here we generalize the convergence result of (Comm. Math. Sci. 8 (2010), 463–479) where the same problem is treated without the oscillating electrostatic potential and we extend the one dimensional result of (Ann. Henri Poincaré 17 (2016), 2529–2553) to the case of several space dimensions. An averaging lemma and two scale convergence techniques are used to prove rigorously the convergence of the scaled Vlasov–Poisson–Fokker–Planck system to a homogenized Drift-Diffusion-Poisson system.

中文翻译：

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Vlasov-Poisson-Fokker-Planck系统的均质化和扩散近似：相对熵方法

我们关注的是通过Vlasov-Poisson-Fokker-Planck系统的扩散和均质化进行的近似分析。在这里，我们概括了（Comm。Math。Sci。8（2010），463–479）的收敛结果，其中，相同的问题在没有振荡的静电势的情况下得到了解决，并且我们扩展了（Ann。HenriPoincaré17（2016 ），2529–2553）到多个空间尺寸的情况。平均引理和两种尺度收敛技术被用来严格证明尺度的Vlasov-Poisson-Fokker-Planck系统到均质的Drift-Diffusion-Poisson系统的收敛。