Diffusion Limit and the optimal convergence rate of the Vlasov-Poisson-Fokker-Planck system

TL;DR

This paper investigates how solutions to the Vlasov-Poisson-Fokker-Planck system behave in the diffusion limit, establishing the optimal convergence rate to the drift-diffusion-Poisson system using spectral analysis.

Contribution

It provides a rigorous proof of convergence and determines the optimal rate for the diffusion limit of the VPFP system near a Maxwellian.

Findings

Proves convergence of VPFP solutions to drift-diffusion-Poisson system

Establishes the optimal convergence rate

Analyzes initial layer effects with spectral methods

Abstract

In the present paper, we study the diffusion limit of the classical solution to the Vlasov-Poisson-Fokker-Planck (VPFP) system with initial data near a global Maxwellian. We prove the convergence and establish the optimal convergence rate of the global strong solution to the VPFP system towards the solution to the drift-diffusion-Poisson system based on the spectral analysis with precise estimation on the initial layer.