Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-24T04:09:24.965Z Has data issue: false hasContentIssue false
  • English
  • Français

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. ([email protected])
Mario Pulvirenti
Affiliation:
Dipartimento di Matematica, Università di Roma "La Sapienza" , P.ale A. Moro 2, 00185 Rome, Italy. ([email protected])
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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