Meccanica

, Volume 20, Issue 3, pp 249–252

# The semidiscrete Boltzmann equation for hard-spheres

• Giuseppe Toscani
Brief Notes

## Summary

This paper deals with a semi-discrete model of the Boltzmann equation, such that the velocity distribution is discretized in modulus, but non in direction. The mathematical model is described in details, then the formulation of the initial value problem is proposed; the mathematical analysis supplies some rigorous results on the global mild solution and on its asymptotic behaviour.

## Keywords

Mathematical Model Mechanical Engineer Civil Engineer Asymptotic Behaviour Velocity Distribution
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.

## Sommario

Si studia un modello di equazione di Boltzmann semidiscreta, caratterizzato dal fatto che le velocità sono discretizzate in modulo e non in direzione. Viene descritto in dettaglio il modello, quindi si studia il problema di Cauchy, fornendo indicazioni sul comportamento asintotico della soluzione.

## References

1. [1]
Cabannes H.:The discrete Boltzmann equation: theory and application. College of Eng.ng, University of Berkeley (1980).Google Scholar
2. [2]
Gatignol R.:Thèorie cinétique des gaz à repartition discrète de vitèness. Lecture Notes in Phys. n. 36 (1976).Google Scholar
3. [3]
Bellomo N., Illner R., Toscani G.:Sur le problème de Cauchy pour l'équation de Boltzmann semi-discrète, C.R.A.S. Settembre 1984.Google Scholar
4. [4]
Toscani G.:On the discrete velocity models of the Boltzmann equation in several dimensions. Annali Matem. Pura ed Appl. (1984), 297–308.Google Scholar
5. [5]
Bellomo N., Toscani G.:On the Cauchy problem for the non-linear Boltzmann equation: Global existence, uniqueness and asymptotical stability. Journal of Math. Phys, 26 (2), (1985), 334–338.
6. [6]
Cercignani C.:Theory and application of the Boltzmann equation, Scottish Academic Press, Edinburgh (1975).Google Scholar
7. [7]
Toscani G.:Global existence and asymptotic behaviour for the discrete velocity model of the Boltzmann equation, Proceedings of the «Workshop on Mathematical Aspects of Fluid and Plasma Dynamics» Ed. Tessarotto, Trieste (1984).Google Scholar