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Teoreticheskaya i Matematicheskaya Fizika, 2005, Volume 143, Number 3, Pages 437–454
DOI: https://doi.org/10.4213/tmf1824 (Mi tmf1824) 		 
This article is cited in 5 scientific papers (total 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
Full-text PDF (238 kB) Citations (5)
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DOI: https://doi.org/10.4213/tmf1824
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
English version:
Theoretical and Mathematical Physics, 2005, Volume 143, Issue 3, Pages 854–869
DOI: https://doi.org/10.1007/s11232-005-0111-0
Bibliographic databases:
Language: Russian
Citation: A. V. Latyshev, A. A. Yushkanov, “The Method of Singular Equations in Boundary Value Problems in Kinetic Theory”, TMF, 143:3 (2005), 437–454; Theoret. and Math. Phys., 143:3 (2005), 854–869
Citation in format AMSBIB
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\paper The Method of Singular Equations in Boundary Value Problems in Kinetic Theory
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\jour Theoret. and Math. Phys.
\yr 2005
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\pages 854--869
\crossref{https://doi.org/10.1007/s11232-005-0111-0}
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Linking options:
  • https://www.mathnet.ru/eng/tmf1824
  • https://doi.org/10.4213/tmf1824
  • https://www.mathnet.ru/eng/tmf/v143/i3/p437
    • This publication is cited in the following 5 articles:
    1. O V Germider, V N Popov, “A collocation method for the Williams equation with Chebyshev polynomials”, J. Phys.: Conf. Ser., 2056:1 (2021), 012005  crossref
    2. V N Popov, I V Popov, “Analytical solution to the problem of diffusion of the light component of the binary gas mixture in a plane channel”, J. Phys.: Conf. Ser., 2056:1 (2021), 012004  crossref
    3. A. V. Latyshev, A. A. Yushkanov, “Novyi metod resheniya granichnykh zadach kineticheskoi teorii”, Zh. vychisl. matem. i matem. fiz., 52:3 (2012), 539–552  mathnet  zmath  elib
    4. Latyshev AV, Yushkanov AA, “Current flowing through a boundary between crystallites at arbitrary coefficients of transmission and specular reflection”, Physics of Metals and Metallography, 103:1 (2007), 23–32  crossref  mathscinet  adsnasa  isi  scopus  scopus
    5. A. V. Latyshev, A. A. Yushkanov, “Couette problem for a rarefied gas in a channel”, J Eng Phys Thermophys, 79:2 (2006), 403  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:90
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