Diffusion limit and the optimal convergence rate of the Vlasov-Poisson-Fokker-Planck system | Zendy

Mingying Zhong | Zendy

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

Author(s) -

Mingying Zhong

Publication year - 2021

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.

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