Advertisement

Preliminary results on the non-existence of solutions for a half space boltzmann collision model with three degrees of freedom

  • M. D. Arthur
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1048)

Abstract

A two component model of the linearized Boltzmann equation in a half-space incorporating three degrees of freedom is studied. The linearized collision term is taken to be a summation over a suitable combination of the collision invariants. Preliminary results concerning exponents of compensating factors involved in the Wiener-Hopf factorization of the dispersion matrix are presented. Comparison is made to the case of the linearized Boltzmann equation in a half-space incorporating only one degree of freedom.

Keywords

Boltzmann Equation Real Axis Speed Ratio Analyticity Requirement Transport Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Tor Ytrehus, article in this volume.Google Scholar
  2. 2.
    Wang Chang, C. S. and G. E. Uhlenbeck, Dept. of Engr. Research report, U. of Mich., 1952.Google Scholar
  3. 3.
    C. Cercignani, Theory and Application of the Boltzmann Equation, Scottish Academic Press, Edinburgh, and Elsevier, New York (1975).zbMATHGoogle Scholar
  4. 4.
    Gross, E. P. and Jackson, E. A., Phys. Fluids 2, 4, 432, (1959).ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    M. D. Arthur and C. Cercignani, J. Appl. Math. and Phys. (ZAMP) Vol. 31, 634, (1980).MathSciNetCrossRefGoogle Scholar
  6. 6.
    C. Cercignani, Elementary Solutions of Linearized Kinetic Models and Boundary Value Problems in the Kinetic Theory of Gases, Div. of Appl. Math. and Engr. report, Brown University, Providence, Rhode Island (1965).Google Scholar
  7. 7.
    E. W. Larsen and G. Habetler, Commun. Pure Appl. Math. 26, 525 (1973).MathSciNetCrossRefGoogle Scholar
  8. 8.
    E. W. Larsen, Commun. Pure Appl. Math. 28, 729 (1975).CrossRefGoogle Scholar
  9. 9.
    E. W. Larsen, S. Sancaktar and P. F. Zweifel, J. Math. Phys. 16, 117 (1976).MathSciNetGoogle Scholar
  10. 10.
    H. Grad, Handbuch der Physik, 12, sec. 19, (1958).Google Scholar
  11. 11.
    H. Hejtmanek, article in this volume.Google Scholar
  12. 12.
    M. D. Arthur and C. Cercignani, On the Riemann-Hilbert Problem for \(\mathop \Omega \limits_ \approx\), in preparation.Google Scholar
  13. 13.
    Dunford, N. and Schwartz, J. T., Linear Operators, Wiley, New York (1964).zbMATHGoogle Scholar
  14. 14.
    K. M. Case, Ann. Phys. 9, 1 (1960).ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    P. F. Zweifel, R. L. Bowden and W. Greenberg, J. Math. Phys. 5, 219 (1979).MathSciNetGoogle Scholar
  16. 16.
    M. D. Arthur, Ph. D. dissertation, available from University Microfilms, Inc., Ann Arbor, Mich. (1979).Google Scholar
  17. 17.
    C. Cercignani, Proc. Oberwolfach Conference on Math. Problems in Kinetic Theory, May 1979 (1980).Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • M. D. Arthur
    • 1
  1. 1.Abteilung für Mathematische PhysikUniversität UlmGermany

Personalised recommendations