Kinetic and hydrodynamic equations for granular media

Mario Pulvirenti

Journées équations aux dérivées partielles (1999)

  • page 1-8
  • ISSN: 0752-0360

Abstract

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In this lecture i present some open mathematical problems concerning some PDE arising in the study of one-dimensional models for granular media.

How to cite

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Pulvirenti, Mario. "Kinetic and hydrodynamic equations for granular media." Journées équations aux dérivées partielles (1999): 1-8. <http://eudml.org/doc/93368>.

@article{Pulvirenti1999,
abstract = {In this lecture i present some open mathematical problems concerning some PDE arising in the study of one-dimensional models for granular media.},
author = {Pulvirenti, Mario},
journal = {Journées équations aux dérivées partielles},
language = {eng},
pages = {1-8},
publisher = {Université de Nantes},
title = {Kinetic and hydrodynamic equations for granular media},
url = {http://eudml.org/doc/93368},
year = {1999},
}

TY - JOUR
AU - Pulvirenti, Mario
TI - Kinetic and hydrodynamic equations for granular media
JO - Journées équations aux dérivées partielles
PY - 1999
PB - Université de Nantes
SP - 1
EP - 8
AB - In this lecture i present some open mathematical problems concerning some PDE arising in the study of one-dimensional models for granular media.
LA - eng
UR - http://eudml.org/doc/93368
ER -

References

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  1. [A] L. ArkerydExistence theorems for certain kinetic equations Arch Rat Mech and Anal 103 pp 139-149, (1988). Zbl0654.76073MR89h:82014
  2. [B] M. BonySolutions globales bornées pour le modèles discrets de l'équation de Boltzmann en dimension 1 d'espace Act. Jour. E.D.P. St. Jean de Monts (1987). 
  3. [BC] D. Benedetto, E. CagliotiCollapse for one-dimensional granular media preprint Roma (1998). 
  4. [BCCP] D. Benedetto, E. Caglioti, J.A. Carrillo, M. PulvirentiA non Maxwellian equilibrium distribution for one-dimensional granular media, Jour. Stat. Phys. 91 pp 979-990 (1998). Zbl0921.60057MR2000d:82035
  5. [BCGP] D. Benedetto, E. Caglioti, F. Golse, M. PulvirentiA Hydrodynamic Model Arising in the Context of Granular Media, preprint Roma (1998). Zbl0946.76096
  6. [BCP] D. Benedetto, E. Caglioti and M. PulvirentiA Kinetic Equation for Granular Media, Math. Mod. and Num. An. 31 n. 5, pp 615-641 (1997). Zbl0888.73006MR98k:82145
  7. [BCPe] D. Benedetto, E. Caglioti and M. PulvirentiA Kinetic Equation for Granular Media : erratum, (to appear). Zbl0972.74017
  8. [BCP2] D. Benedetto, E. Caglioti, M. PulvirentiA one dimensional Boltzmann equation with inelastic collisions, (in press on Rend. Sem. Mat. Fis. Milano 1998). 
  9. [BM] B. Bernu and R. MazighiOne-dimensional bounce of inelastically colliding marbles on a wall, Jour. of Phys. A : Math. Gen. 23 pp. 5745-5754 (1990). Zbl0729.73648
  10. [C] S. CampbellRapid Granular Flows, Ann. Rev. of Fluid Mech. 22 pp. 57-92 (1990). 
  11. [CGM] P. Constantin, E. Grossman, M. MunganInelastic collisions of three particles on a line as a two-dimensional billiard, Physica D 83 pp. 409-420 (1995). Zbl0900.70198MR96k:70011
  12. [DLK] Y. Du, H. Li, L. P. Kadanoff, Breakdown of Hydrodynamics in One-Dimensional System of Inelastic Particles, Phys. Rev. Lett. 74 (8), pp. 1268-1271, (1995). 

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