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A boundary‐value problem for the stationary vlasov‐poisson equations: The plane diode
Author(s) -
Greengard Claude,
Raviart P.A.
Publication year - 1990
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160430404
Subject(s) - uniqueness , mathematics , boundary value problem , mathematical analysis , bounded function , plane (geometry) , domain (mathematical analysis) , boundary (topology) , mixed boundary condition , poisson's equation , uniqueness theorem for poisson's equation , geometry
The stationary Vlasov‐Poisson boundary value problem in a spatially one‐dimensional domain is studied. The equations describe the flow of electrons in a plane diode. Existence is proved when the boundary condition (the cathode emission distribution) is a bounded function which decays super‐linearly or a Dirac mass. Uniqueness is proved for (physically realistic) boundary conditions which are decreasing functions of the velocity variable. It is shown that uniqueness does not always hold for the Dirac mass boundary conditions.