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1987•Mathematical Methods in the Applied SciencesRequires access

Stationary solutions of the vlasov‐fokker‐planck equation

Klaus Dreßler, Helmut Neunzert

Open publisher page 26 citations

Abstract

Abstract We study stationary solutions of the Vlasov‐Fokker‐Planck Equation, a modification of the Vlasov‐Poisson Equation, obtained by adding a diffusion term with respect to velocity. From a physical point of view it describes a plasma in thermal equilibrium. We prove existence of stationary solutions; for the mollified equation even an existence‐ and uniqueness theorem holds for sufficiently high temperature.

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Abstract We study stationary solutions of the Vlasov‐Fokker‐Planck Equation, a modification of the Vlasov‐Poisson Equation, obtained by adding a diffusion term with respect to velocity. From a physical point of view it describes a plasma in thermal equilibrium. We prove existence of stationary solutions; for the mollified equation even an existence‐ and uniqueness theorem holds for sufficiently high temperature.

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Available abstract

Abstract We study stationary solutions of the Vlasov‐Fokker‐Planck Equation, a modification of the Vlasov‐Poisson Equation, obtained by adding a diffusion term with respect to velocity. From a physical point of view it describes a plasma in thermal equilibrium. We prove existence of stationary solutions; for the mollified equation even an existence‐ and uniqueness theorem holds for sufficiently high temperature.

Key concepts: Fokker–Planck equation, Vlasov equation, Uniqueness, Mathematics, Uniqueness theorem for Poisson's equation, Stationary solution, Diffusion, Mathematical physics

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