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L ∞ ‐estimates for the Vlasov–Poisson–Fokker–Planck equation
Author(s) -
Pulvirenti M.,
Simeoni C.
Publication year - 2000
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/1099-1476(20000710)23:10<923::aid-mma143>3.0.co;2-r
Subject(s) - fokker–planck equation , mathematics , vlasov equation , diffusion , diffusion process , poisson distribution , statistical physics , poisson's equation , diffusion equation , mathematical physics , mathematical analysis , plasma , partial differential equation , physics , innovation diffusion , statistics , quantum mechanics , knowledge management , economy , computer science , economics , service (business)
We consider the Vlasov–Poisson–Fokker–Planck equation in three dimensions as the backward Kolmogorov equation associated to a non‐linear diffusion process. In this way we derive new L ∞ ‐estimates on the spatial density which are uniform in the diffusion parameters. Copyright © 2000 John Wiley & Sons, Ltd.