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Journal of Statistical Physics

, Volume 78, Issue 5–6, pp 1555–1570 | Cite as

Approximation of the Boltzmann equation by discrete velocity models

  • Wolfgang Wagner
Articles

Abstract

Two convergence results related to the approximation of the Boltzmann equation by discrete velocity models are presented. First we construct a sequence of deterministic discrete velocity models and prove convergence (as the number of discrete velocities tends to infinity) of their solutions to the solution of a spatially homogeneous Boltzmann equation. Second we introduce a sequence of Markov jump processes (interpreted as random discrete velocity models) and prove convergence (as the intensity of jumps tends to infinity) of these processes to the solution of a deterministic discrete velocity model.

Key Words

Boltzmann equation discrete velocity models weak convergence random mass flow 

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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Wolfgang Wagner
    • 1
  1. 1.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany

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