Skip to main content
SpringerLink
Log in
Book cover

Modern Mathematical Methods in Transport Theory pp 189–199Cite as

Birkhäuser

Analytic Solution of the Model Boltzmann Equation with the Collision Operator of Compound Type

  • Chapter

  • 235 Accesses

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 51))

Abstract

A closed form solution of a system of two singular integral equations arising in the problem of slip flow in a rarefied gas is presented. The kinetic Boltzmann equation with a model collision operator of compound type is considered. Case’s method and the Riemann Hilbert vector boundary problem with matrix coefficients is used. The solution of the Boltzmann equation in half space along a hard surface is constructed. The exact formula for calculation of the isothermic slip coefficient is obtained.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K.M. Case, “Elementary Solutions of the Transport Equations and Thei Applications,” Ann. Phys. 9, 1–23 (1960).

    Article  Google Scholar 

  2. C. Cercignani, “Elementary Solutions of the linearized Gas-Dynamics Boltzmann Equation and their Application to the Slip-Flow,” Ann. Phys. 20, 219–233 (1962).

    Article  Google Scholar 

  3. C. Cercignani, “Closed-Form Solutions of the temperature jump problem for the BGK model,” TTSP 6, 29–56 (1977).

    Google Scholar 

  4. E.M. Shahov, “A method of construction a kinetic model equations.” In: Computing methods in the mechanics continuum medium, Novosibirski, VC SO AN USSR, V. 4, No. 3, 1972 (in Russian).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics Analysis, Moscow Regional Pedagogical Institute, Moscow, USSR

    A. V. Latyshev

  2. Department of Theoretical Physics, Moscow Regional Pedagogical Institute, Moscow, USSR

    M. N. Gajdukov

  3. Department of Integral Equations, Hydromechanics Institute, Odessa, USSR

    I. M. Spitkovski

Authors
  1. A. V. Latyshev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. N. Gajdukov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. M. Spitkovski
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, Virginia, 24061, USA

    William Greenberg

  2. Dept. of Chemistry and Dept. of Applied Mathematics, SUNY, Stony Brook, New York, 11794, USA

    Jacek Polewczak

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer Basel AG

About this chapter

Cite this chapter

Latyshev, A.V., Gajdukov, M.N., Spitkovski, I.M. (1991). Analytic Solution of the Model Boltzmann Equation with the Collision Operator of Compound Type. In: Greenberg, W., Polewczak, J. (eds) Modern Mathematical Methods in Transport Theory. Operator Theory: Advances and Applications, vol 51. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5675-1_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-5675-1_16

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5677-5

  • Online ISBN: 978-3-0348-5675-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation