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On the one-dimensional Boltzmann equation for granular flows

Published online by Cambridge University Press:  15 April 2002

Dario Benedetto and
Mario Pulvirenti
Dario Benedetto
Affiliation:
Dipartimento di Matematica, Università di Roma "La Sapienza" , P.ale A. Moro 2, 00185 Rome, Italy. (benedetto@mat.uniroma1.it)
Mario Pulvirenti
Affiliation:
Dipartimento di Matematica, Università di Roma "La Sapienza" , P.ale A. Moro 2, 00185 Rome, Italy. (pulvirenti@axcasp.caspur.it)
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Abstract

We consider a Boltzmann equation for inelastic particles on the line and prove existence and uniqueness for the solutions.

Keywords

Inelastic collisionsgranular mediaBoltzmann equation.

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 5 , September 2001, pp. 899 - 905
Copyright
© EDP Sciences, SMAI, 2001

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References

Arkeryd, L., Existence theorems for certain kinetic equations and large data. Arch. Rational Mech. Anal. 103 (1988) 139-149. CrossRef
Benedetto, D., Caglioti, E. and Pulvirenti, M., A kinetic equation for one-dimensional granular media. RAIRO Modél. Math. Anal. Numér. 31 (1997) 615-641. CrossRef
D. Benedetto, E. Caglioti and M. Pulvirenti, A one-dimensional Boltzmann equation with inelastic collisions. Rend. Sem. Mat. Fis. Milano LXVII (1997) 169-179.
J.-M. Bony, Solutions globales bornées pour les modèles discrets de l'équation de Boltzmann en dimension 1 d'espace, in Actes Journées Équ. Dériv. Part. 16 , St.-Jean-de-Monts (1987).
L. Tartar, Existence globale pour un système hyperbolique semi-linéaire de la théorie cinétique des gaz, in Séminaire Goulaouic-Schwartz 1975-76, Équat. Dériv. Part. Anal. Fonct., Exposé I, École Polytechnique, Palaiseau (1976).
Toscani, G., One-dimensional kinetic models of granular flows. Math. Model. Numer. Anal. 34 (2000) 1277-1291. CrossRef