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Communications in Mathematical Physics

, Volume 105, Issue 2, pp 205–219 | Cite as

On the Boltzmann equation in unbounded space far from equilibrium, and the limit of zero mean free path

  • Leif Arkeryd
Article

Abstract

This paper studies Loeb solutions of the Boltzmann equation in unbounded space under natural initial conditions of finite mass, energy, and entropy. An existence theory for large initial data is presented. Maxwellian behaviour is obtained in the limits of zero mean free path and of infinite time. In the standard, space-homogeneous, hard potential case, the infinite time limit is of strongL1 type.

Keywords

Entropy Neural Network Statistical Physic Complex System Initial Data 
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.

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References

  1. [AFHL]
    Albeverio, S., Fenstad, J. E., Høegh-Krohn, R., Lindstrøm, T.: Nonstandard methods in stochastic analysis and mathematical physics. New York: Academic Press 1986Google Scholar
  2. [A1]
    Arkeryd, L.: On the Boltzmann equation. Arch. Ration. Mech. Anal.45, 1–34 (1972)Google Scholar
  3. [A2]
    Arkeryd, L.: An existence theorem for a modified space-inhomogeneous, non-linear Boltzmann equation. Bull. Am. Math. Soc.78, 610–614 (1972)Google Scholar
  4. [A3]
    Arkeryd, L.: Loeb solutions of the Boltzmann equation. Arch. Ration. Mech. Anal.86, 85–97 (1984)Google Scholar
  5. [C]
    Cercignani, C.: Theory and application of the Boltzmann equation. New York: Academic Press 1975Google Scholar
  6. [E]
    Elmroth, T.: The Boltzmann equation; on existence and qualitative properties. Dissertation, Chalmers University of Technology 1984Google Scholar
  7. [L]
    Loeb, P. A.: conversion from non-standard measure spaces and applications in probability theory. Trans. Am. Math. Soc.211, 113–122 (1975)Google Scholar
  8. [TM]
    Truesdell, C., Muncaster, R. G.: Fundamentals of Maxwell's kinetic theory of a simple monatomic gas. New York: Academic Press 1980Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Leif Arkeryd
    • 1
  1. 1.Department of MathematicsChalmers University of Technology and University of GöteborgGöteborgSweden

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