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Some probabilistic problems in the spatially homogeneous Boltzmann equation

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Theory and Application of Random Fields

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 49))

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References

  1. M. Kac, Foundations of kinetic theory, Proc. Third Berkeley Symp. on Math. Stat. and Prob., 3(1956), 171–197.

    Google Scholar 

  2. M. Kac, Some probabilistic aspects of the Boltzmann-equation, Acta Physica Austriaca, Suppl. X(1973), 379–400.

    Google Scholar 

  3. H. P. McKean, An exponential formula for solving Boltzmann's equation for a Maxwellian gas, J. Combinatorial Theory, 2(1967), 358–382.

    Google Scholar 

  4. H. P. McKean, Fluctuations in the kinetic theory of gases, Comm. Pure Appl. Math., 28(1975), 435–455.

    Google Scholar 

  5. F. A. Grünbaum, Propagation of chaos for the Boltzmann equation, Arch. Rational Mech. Anal., 42(1971), 323–345.

    Google Scholar 

  6. H. Murata, Propagation of chaos for Boltzmann-like equation of non-cutoff type in the plane, Hiroshima Math. J., 7(1977), 479–515.

    Google Scholar 

  7. H. Tanaka, Fluctuation theory for Kac's one-dimensional model of Maxwellian molecules, to appear in Sankhyā, 44, Series A, Part I (1982).

    Google Scholar 

  8. K. Uchiyama, Fluctuations of Markovian systems in Kac's caricature of a Maxwellian gas, to appear in J. Math. Soc. Japan.

    Google Scholar 

  9. K. Uchiyama, A Fluctuation problem associated with the Boltzmann equation for a gas of molecules with a cut-off potential, to appear.

    Google Scholar 

  10. L. Arkeryd, On the Boltzmann equation, Part I, II, Archive for Rational Mech. Anal., 45(1972), 1–16, 17–34.

    Google Scholar 

  11. C. S. Wang Chang and G. E. Uhlenbeck (1952), In "The Kinetic Theory of Gases", Studies in Statistical Mechanics, Vol. V, North-Holland, Amsterdam (1970).

    Google Scholar 

  12. C. Cercignani, Mathematical Methods in Kinetic Theory, Plenum Press, New York (1969).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics Faculty of Science and Technology, Keio University, Yokohama, Japan

    Hiroshi Tanaka

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  1. Hiroshi Tanaka
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G. Kallianpur

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© 1983 Springer-Verlag

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Tanaka, H. (1983). Some probabilistic problems in the spatially homogeneous Boltzmann equation. In: Kallianpur, G. (eds) Theory and Application of Random Fields. Lecture Notes in Control and Information Sciences, vol 49. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0044698

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  • DOI: https://doi.org/10.1007/BFb0044698

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12232-6

  • Online ISBN: 978-3-540-39564-5

  • eBook Packages: Springer Book Archive

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