On the one-dimensional Boltzmann equation for granular flows

Dario Benedetto; Mario Pulvirenti

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 35, Issue: 5, page 899-905
  • ISSN: 0764-583X

Abstract

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

How to cite

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Benedetto, Dario, and Pulvirenti, Mario. "On the one-dimensional Boltzmann equation for granular flows." ESAIM: Mathematical Modelling and Numerical Analysis 35.5 (2010): 899-905. <http://eudml.org/doc/197601>.

@article{Benedetto2010,
abstract = { We consider a Boltzmann equation for inelastic particles on the line and prove existence and uniqueness for the solutions. },
author = {Benedetto, Dario, Pulvirenti, Mario},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Inelastic collisions; granular media; Boltzmann equation.; inelastic collisions; Boltzmann equation},
language = {eng},
month = {3},
number = {5},
pages = {899-905},
publisher = {EDP Sciences},
title = {On the one-dimensional Boltzmann equation for granular flows},
url = {http://eudml.org/doc/197601},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Benedetto, Dario
AU - Pulvirenti, Mario
TI - On the one-dimensional Boltzmann equation for granular flows
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 5
SP - 899
EP - 905
AB - We consider a Boltzmann equation for inelastic particles on the line and prove existence and uniqueness for the solutions.
LA - eng
KW - Inelastic collisions; granular media; Boltzmann equation.; inelastic collisions; Boltzmann equation
UR - http://eudml.org/doc/197601
ER -

References

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  1. L. Arkeryd, Existence theorems for certain kinetic equations and large data. Arch. Rational Mech. Anal.103 (1988) 139-149.  Zbl0654.76073
  2. D. Benedetto, E. Caglioti and M. Pulvirenti, A kinetic equation for one-dimensional granular media. RAIRO Modél. Math. Anal. Numér.31 (1997) 615-641.  Zbl0888.73006
  3. D. Benedetto, E. Caglioti and M. Pulvirenti, A one-dimensional Boltzmann equation with inelastic collisions. Rend. Sem. Mat. Fis. Milano LXVII (1997) 169-179.  Zbl1011.82019
  4. 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).  
  5. 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).  Zbl0336.35069
  6. G. Toscani, One-dimensional kinetic models of granular flows. Math. Model. Numer. Anal.34 (2000) 1277-1291.  Zbl0981.76098

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