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JOURNALS // Teoreticheskaya i Matematicheskaya Fizika // Archive

TMF, 2005 Volume 143, Number 3, Pages 437–454 (Mi tmf1824)

This article is cited in 5 papers

The Method of Singular Equations in Boundary Value Problems in Kinetic Theory

A. V. Latyshev, A. A. Yushkanov

Moscow State Region University

Abstract: We develop a new effective method for solving boundary value problems in kinetic theory. The method permits solving boundary value problems for mirror and diffusive boundary conditions with an arbitrary accuracy and is based on the idea of reducing the original problem to two problems of which one has a diffusion boundary condition for the reflection of molecules from the wall and the other has a mirror boundary condition. We illustrate this method with two classical problems in kinetic theory: the Kramers problem (isothermal slip) and the thermal slip problem. We use the Bhatnagar–Gross–Krook equation (with a constant collision frequency) and the Williams equation (with a collision frequency proportional to the molecular velocity).

Keywords: boundary value problem, kinetic equation, Kramers problem, thermal slip problem, isothermal slip coefficient, thermal slip coefficient.

Received: 28.09.2004
Revised: 26.11.2004

DOI: 10.4213/tmf1824


 English version:
Theoretical and Mathematical Physics, 2005, 143:3, 854–869

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