Skip to main content
SpringerLink
Log in

The full lie group and invariant solutions of the system of boltzmann equations of a multicomponent gas mixture

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. A. V. Bobylev, “On exact solutions to the Boltzmann equation,” Dokl. Akad. Nauk SSSR,225, No. 5, 1296–1299 (1975).

    MathSciNet  Google Scholar 

  2. M. Krook and T. T. Wu, “Formation of Maxwellian tails,” Phys. Rev. Lett.,36, No. 19, 1107–1109 (1976).

    Article  Google Scholar 

  3. M. H. Ernst, “Nonlinear model-Boltzmann equations and exact solutions,” Phys. Rep.,78, No. 1, 1–171 (1981).

    Article  MathSciNet  Google Scholar 

  4. J. L. Lebowitz and E. W. Montroll (eds.), Nonequilibrium Phenomena. I. The Boltzmann Equation, North-Holland Publishing Co., Amsterdam and New York (1983).

    MATH  Google Scholar 

  5. M. H. Ibragimov (ed.), CRC Handbook of Lie Group Analysis of Differential Equations. Vol. 1–3, CRC Press, 1992–1995.

  6. L. V. Ovsyannikov, Group Analysis of Differential Equations [in Russian], Nauka, Moscow (1978).

    MATH  Google Scholar 

  7. Yu. N. Grigor’ev and S. V. Meleshko, “Group analysis of the integro-differential Boltzmann equation,” Dokl. Akad. Nauk SSSR,297, No. 2, 323–327 (1987).

    MathSciNet  Google Scholar 

  8. Yu. N. Grigoryev and S. V. Meleshko, “Group analysis of kinetic equations,” Russian J. Numer. Anal. Math. Modelling,10, No. 5, 425–447 (1995).

    Article  MathSciNet  Google Scholar 

  9. M. Krook and T. T. Wu, “Exact solution of Boltzmann equations for multicomponent systems,” Phys. Rev. Lett.,38, No. 18, 991–993 (1977).

    Article  Google Scholar 

  10. A. V. Bobylev, “The structure of spatially uniform normal solutions of the nonlinear Boltzmann equation for a gas mixture,” Dokl. Akad. Nauk SSSR,250, No. 2, 340–344 (1980).

    MathSciNet  Google Scholar 

  11. J. H. Ferziger and H. G. Kaper, Mathematical Theory of Transport Processes in Gases [Russian translation], Mir, Moscow (1976).

    Google Scholar 

  12. G. Korn and T. Korn, Handbook on Mathematics [in Russian], Nauka, Moscow (1973).

    Google Scholar 

Download references

Authors
  1. Yu. N. Grigor’ev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. V. Meleshko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The research was partially supported by the Russian Foundation for Basic Research (Grant 96-01-01642).

Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 38, No. 3, pp. 510–525, May–June, 1997.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grigor’ev, Y.N., Meleshko, S.V. The full lie group and invariant solutions of the system of boltzmann equations of a multicomponent gas mixture. Sib Math J 38, 434–448 (1997). https://doi.org/10.1007/BF02683832

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02683832

Keywords

Search

Navigation