Open AccessDiffusion limit and the optimal convergence rate of the Vlasov-Poisson-Fokker-Planck system
Author(s) -
Mingying Zhong
Publication year - 2022
Publication title -
kinetic and related models
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.987
H-Index - 28
eISSN - 1937-5093
pISSN - 1937-5077
DOI - 10.3934/krm.2021041
Subject(s) - fokker–planck equation , diffusion , limit (mathematics) , convergence (economics) , rate of convergence , poisson distribution , statistical physics , physics , vlasov equation , mathematics , mathematical analysis , plasma , computer science , quantum mechanics , partial differential equation , statistics , economics , computer network , channel (broadcasting) , economic growth
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.