Kinetic and hydrodynamic equations for granular media
Journées équations aux dérivées partielles, (1999), article no. 11, 8 p.

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

@article{JEDP_1999____A11_0,
     author = {Pulvirenti, Mario},
     title = {Kinetic and hydrodynamic equations for granular media},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     publisher = {Universit\'e de Nantes},
     year = {1999},
     mrnumber = {1718990},
     zbl = {01810584},
     mrnumber = {2000h:74026},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_1999____A11_0}
}
Pulvirenti, Mario. Kinetic and hydrodynamic equations for granular media. Journées équations aux dérivées partielles,  (1999), article  no. 11, 8 p. http://www.numdam.org/item/JEDP_1999____A11_0/

[A] L. Arkeryd Existence theorems for certain kinetic equations Arch Rat Mech and Anal 103 pp 139-149, (1988). | MR 89h:82014 | Zbl 0654.76073

[B] M. Bony Solutions 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). | Numdam

[BC] D. Benedetto, E. Caglioti Collapse for one-dimensional granular media preprint Roma (1998).

[BCCP] D. Benedetto, E. Caglioti, J.A. Carrillo, M. Pulvirenti A non Maxwellian equilibrium distribution for one-dimensional granular media, Jour. Stat. Phys. 91 pp 979-990 (1998). | MR 2000d:82035 | Zbl 0921.60057

[BCGP] D. Benedetto, E. Caglioti, F. Golse, M. Pulvirenti A Hydrodynamic Model Arising in the Context of Granular Media, preprint Roma (1998). | Zbl 0946.76096

[BCP] D. Benedetto, E. Caglioti and M. Pulvirenti A Kinetic Equation for Granular Media, Math. Mod. and Num. An. 31 n. 5, pp 615-641 (1997). | Numdam | MR 98k:82145 | Zbl 0888.73006

[BCPe] D. Benedetto, E. Caglioti and M. Pulvirenti A Kinetic Equation for Granular Media : erratum, (to appear). | Numdam | Zbl 0972.74017

[BCP2] D. Benedetto, E. Caglioti, M. Pulvirenti A one dimensional Boltzmann equation with inelastic collisions, (in press on Rend. Sem. Mat. Fis. Milano 1998).

[BM] B. Bernu and R. Mazighi One-dimensional bounce of inelastically colliding marbles on a wall, Jour. of Phys. A : Math. Gen. 23 pp. 5745-5754 (1990). | Zbl 0729.73648

[C] S. Campbell Rapid Granular Flows, Ann. Rev. of Fluid Mech. 22 pp. 57-92 (1990).

[CGM] P. Constantin, E. Grossman, M. Mungan Inelastic collisions of three particles on a line as a two-dimensional billiard, Physica D 83 pp. 409-420 (1995). | MR 96k:70011 | Zbl 0900.70198

[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).