Skip to main content
Log in

Zur Boltzmanngleichung

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

The existence theory for the nonlinear Boltzmann equation is discussed for an infinite region in the spatially homogeneous case. We show that the solution is given by a nonlinear contraction semigroup. It is found that theH-theorem holds and that the system approaches equilibrium.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

Literatur

  1. Povzner, A. Ya.: Zur Boltzmanngleichung in der kinetischen Theorie der Gase. Mat. Sb.58, 65–86 (1962).

    Google Scholar 

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

    Google Scholar 

  3. Dorroh, J. R.: Some classes of semi-groups of nonlinear transformations and their generators. J. Math. Soc. Japan20 (3), 437–455 (1968).

    Google Scholar 

  4. Bourbaki, N.: Intégration, chapitres 1, 2, 3 et 4. Paris: Hermann 1965.

    Google Scholar 

  5. Bourbaki, N.: Intégration, chapitre 5. Paris: Hermann 1967.

    Google Scholar 

  6. Yosida, K.: Functional analysis. Berlin-Heidelberg-New York: Springer 1968.

    Google Scholar 

  7. McKean, H. P.: Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas. Arch. Rational Mech. Anal.21, 343–367 (1966).

    Google Scholar 

  8. Morgenstern, D.: Analytical studies related to the Maxwell-Boltzmann equation. J. Rational Mech. Anal.4, 533–555 (1955).

    Google Scholar 

  9. Trotter, H. F.: Approximation of semi-groups of operators. Pacific J. Math.8 (4), 887–919 (1958).

    Google Scholar 

  10. Dieudonné, J.: Foundations of modern analysis. New York: Academic Press 1960.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bodmer, R. Zur Boltzmanngleichung. Commun.Math. Phys. 30, 303–334 (1973). https://doi.org/10.1007/BF01645507

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01645507

Navigation