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Steady States of the Vlasov–Poisson–Fokker–Planck System

✍ Scribed by Robert Glassey; Jack Schaeffer; Yuxi Zheng

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
188 KB
Volume
202
Category
Article
ISSN
0022-247X

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✦ Synopsis

The form of steady state solutions to the Vlasov᎐Poisson᎐Fokker᎐Planck system is known from the works of Dressler and others. In these papers an external < < potential is present which tends to infinity as x ª ϱ. It is shown here that this assumption is needed to obtain nontrivial steady states. This is achieved by showing that for a given nonnegative background density satisfying certain integrability conditions, only the trivial solution is possible. This result is sharp and exactly Ž matches the known existence criteria of F. Bouchut and J. Dolbeault Differential . Integral Equations 8, 1995, 487᎐514 and others. These steady states are solutions to a nonlinear elliptic equation with an exponential nonlinearity. For a given background density which is asymptotically constant, it is directly shown by elementary means that this nonlinear elliptic equation possesses a smooth and uniquely determined global solution.

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