Il Nuovo Cimento B (1971-1996)

, Volume 106, Issue 1, pp 9–20 | Cite as

On exact solutions to a discrete-velocity model of the extended kinetic equations

  • S. Oggioni
  • G. Spiga


The discrete-velocity models of the extended kinetic equations are analysed for the case of a gas of test particles scattering between themselves and absorbed or generated by a background medium. Exact analytical solutions to the set of hyperbolic semilinear first-order PDE governing the components of the particle distribution function are investigated. Particular solutions of different type satisfying special initial conditions are determined or discussed.

PACS 05.20. Dd

Kinetic theory PACS 51.10 Kinetic and transport theory 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    T. Platkowski andR. Illner:SIAM (Soc. Ind. Appl. Math.) Rev.,30, 213 (1988).MathSciNetGoogle Scholar
  2. [2]
    E. Longo andR. Monaco:Transp. Theory Stat. Phys.,17, 423 (1988).MathSciNetADSCrossRefMATHGoogle Scholar
  3. [3]
    G. Borgioli, R. Monaco andG. Toscani: Report 8/1989, Politecnico di Torino.Google Scholar
  4. [4]
    N. Bellomo andS. Kawashima: Report 17/1989, Politecnico di Torino.Google Scholar
  5. [5]
    R. Monaco, M. Pandolfi Bianchi andT. Platkowski:Shock-waves formation by the discrete Boltzmann equation for binary gas mixtures, inActa Mechanica, in press.Google Scholar
  6. [6]
    J. M. Greenberg andL. L. Aist:Arch. Ration. Mech. Anal., submitted for publication.Google Scholar
  7. [7]
    G. Spiga:Rigorous solution to the extended kinetic equations for homogeneous gas mixtures, inIII International Workshop «Mathematical Aspects of Fluid and Plasma Dynamics» in press asSpringer Lecture Notes in Mathematics.Google Scholar
  8. [8]
    G. Spiga, G. Dukek andV. C. Boffi:Scattering kernel formulation of the discrete velocity model of the extended Boltzmann system inDiscrete Kinetic Theory, Lattice Gas Dynamics and Foundation of Hydrodynamics, edited byR. Monaco (World Scientific, Singapore, 1989), p. 315.Google Scholar
  9. [9]
    G. Spiga:Extended kinetic equations for gas mixtures, inXI International Transport Theory Conference, Blacksburg, May 1989, in press.Google Scholar
  10. [10]
    H. Cornille:J. Phys. A,20, 1973 (1987).MathSciNetADSCrossRefMATHGoogle Scholar
  11. [11]
    H. Cornille:J. Math. Phys.,29, 1667 (1988).MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    H. Cornille:J. Math. Phys.,30, 789 (1989).MathSciNetADSCrossRefMATHGoogle Scholar
  13. [13]
    R. Illner:Math. Meth. Appl. Sci.,1, 187 (1979).MathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    V. C. Boffi andK. Aoki:Nuovo Cimento D,10, 1013 (1988).MathSciNetADSCrossRefMATHGoogle Scholar
  15. [15]
    V. C. Boffi, V. Protopopescu andY. Y. Azmy:Nuovo Cimento D,12, 1153 (1990).MathSciNetADSCrossRefMATHGoogle Scholar
  16. [16]
    T. W. Ruijgrok andT. T. Wu:Physica A,113, 401 (1982).MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    M. Abramowitz andI. A. Stegun (Editors).Handbook of Mathematical Functions (Dover, New York, N.Y., 1972).Google Scholar
  18. [18]
    G. M. Murphy:Ordinary Differential Equations and Their Solutions (Van Nostrand, Princeton, N.J., 1960).MATHGoogle Scholar
  19. [19]
    A. A. Nikolskii:Sov. Phys. Dokl.,8, 633 (1964).ADSGoogle Scholar

Copyright information

© Società Italiana di Fisica 1991

Authors and Affiliations

  • S. Oggioni
    • 1
  • G. Spiga
    • 2
  1. 1.Istituto per Ricerche di Matematica Applicata del CNRBariItalia
  2. 2.Dipartimento di Matematica dell’UniversitàBariItalia

Personalised recommendations