Publication
Communications on Pure and Applied Mathematics
Paper

A boundary‐value problem for the stationary vlasov‐poisson equations: The plane diode

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Abstract

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. Copyright © 1990 Wiley Periodicals, Inc., A Wiley Company

Date

17 Oct 2006

Publication

Communications on Pure and Applied Mathematics

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