The density profile for the Klein-Kramers equation near an absorbing wall
type: Item
instance of: scholarly article
title: The density profile for the Klein-Kramers equation near an absorbing wall
zbMATH Open document ID: 0587.60078
DOI: 10.1007/BF01010497
author: U. M. Titulaer
published in: Journal of Statistical Physics
publication date: 1984-01-01T00:00:00Z
review text: We derive asymptotic series for the expansion coefficients of a function in terms of the Pagani functions, which occur in the boundary layer solutions of the Klein-Kramers equation. The results enable us to determine the density profile in the stationary solution of this equation near an absorbing wall from the numerically determined velocity distribution at the wall, with an accuracy of about 2 \%. We also obtain information about the analytic behavior of the density profile: this profile increases near the wall with the square root of the distance to the wall. Finally, the asymptotic analysis leads to an understanding of the slow convergence of variational approximations to the solution of the absorbing-wall problem and of the exponents that occur when one studies the variational approximations to various quantities of interest as functions of the number of terms in the variational ansatz. This is used to obtain a better variational estimate for the density at the wall.
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60J70
zbMATH DE Number: 3942663
zbMATH Keywords: Klein-Kramers equation
zbMATH Keywords: stationary solution
zbMATH Keywords: asymptotic analysis
zbMATH Keywords: absorbing-wall problem
zbMATH Keywords: variational estimate
MaRDI profile type: Publication
cites work: On the Theory of the Brownian Motion II
cites work: The kinetic boundary layer for the Klein-Kramers equation: A new numerical approach
cites work: Half-range completeness for the Fokker-Planck equation. I
cites work: Q4059363
cites work: Q3264312
cites work: Q4092387
cites work: Q3671491
cites work: Q5546685
description: scientific article; zbMATH DE number 3942663