CONVERGENCE OF THE GENERALIZED FUNCTION SOLUTION OF KRAMERS' EQUATION FOR BROWNIAN MOTION.

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Abstract

The generalized function solution of Kramers' equation describing Brownian motion is shown to be valid in type S function spaces of entire functions for at least a finite time. The method also has been applied to the Fokker-Planck equation describing the motion of charged particles undergoing scattering without energy loss. The theoretical results obtained in this paper are expected to guide that development.

Original languageEnglish (US)
Pages (from-to)69-83
Number of pages15
JournalTransport Theory and Statistical Physics
Volume13
Issue number1-2
StatePublished - 1983

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Brownian movement
Fokker-Planck Equation
Entire Function
Generalized Functions
Function Space
Brownian motion
Scattering
Valid
entire functions
function space
Motion
Fokker-Planck equation
Energy
Fokker Planck equation
charged particles
energy dissipation
Charged particles
Energy dissipation
scattering
energy

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

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title = "CONVERGENCE OF THE GENERALIZED FUNCTION SOLUTION OF KRAMERS' EQUATION FOR BROWNIAN MOTION.",
abstract = "The generalized function solution of Kramers' equation describing Brownian motion is shown to be valid in type S function spaces of entire functions for at least a finite time. The method also has been applied to the Fokker-Planck equation describing the motion of charged particles undergoing scattering without energy loss. The theoretical results obtained in this paper are expected to guide that development.",
author = "Ganapol, {Barry D}",
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