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Steady states in plasma physics—the Vlasov–Fokker–Planck equation
Author(s) -
Dressler Klaus
Publication year - 1990
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/mma.1670120603
Subject(s) - vlasov equation , fokker–planck equation , uniqueness , representation (politics) , plasma modeling , plasma , uniqueness theorem for poisson's equation , poisson's equation , mathematics , mathematical physics , physics , statistical physics , mathematical analysis , partial differential equation , differential equation , quantum mechanics , law , politics , political science
In this paper we investigate the non‐linear Vlasov–Fokker–Planck (VFP) equation, a both physically and mathematically interesting modification of Vlasov's equation, which describes a plasma in a thermal bath. We prove existence, uniqueness and representation results for steady states of the VFP equation both in the case of a mollified interaction potential and for the VFP–Poisson system. The uniqueness and representation results are of special interest since they distinguish special solutions of the Vlasov equation.