WIAS Preprint No. 96, (1994)
Approximation of the Boltzmann equation by discrete velocity models
Authors
- Wagner, Wolfgang
2010 Mathematics Subject Classification
- 60K35 76P05 82C40
Keywords
- Boltzmann equation, discrete velocity models, weak convergence, random mass flow
DOI
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.
Appeared in
- J. Statist. Phys., 78 (1995), pp. 1555--1570
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