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On the Vlasov‐Fokker‐Planck equation
Author(s) -
Neunzert H.,
Pulvirenti M.,
Triolo L.
Publication year - 1984
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.1670060134
Subject(s) - vlasov equation , mathematics , fokker–planck equation , uniqueness , limit (mathematics) , poisson's equation , constructive , mathematical analysis , uniqueness theorem for poisson's equation , counterexample , diffusion , plasma , mathematical physics , partial differential equation , physics , quantum mechanics , process (computing) , discrete mathematics , computer science , operating system
Abstract We study a modification of the Vlasov‐Poisson equation, obtained by adding a diffusion term with respect to velocity. It describes, from a physical point of view, a plasma in thermal equilibrium, in a mean field limit situation. We find that the already known results concerning existence and uniqueness of the solutions for the ordinary Vlasov equation (constructive results and counterexamples) translate to our case.