One-dimensional kinetic models of granular flows
Toscani, Giuseppe
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000), p. 1277-1291 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{M2AN_2000__34_6_1277_0,
     author = {Toscani, Giuseppe},
     title = {One-dimensional kinetic models of granular flows},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {34},
     year = {2000},
     pages = {1277-1291},
     mrnumber = {1812737},
     zbl = {0981.76098},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2000__34_6_1277_0}
}

Toscani, Giuseppe. One-dimensional kinetic models of granular flows. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000) pp. 1277-1291. http://gdmltest.u-ga.fr/item/M2AN_2000__34_6_1277_0/

[1] R. Alexandre and C. Villani, On the Boltzmann equation for long range interactions and the Landau approximation in plasma physics. Preprint DMA, École Normale Supérieure (1999).

[2] L. Arkeryd, Intermolecular forces of infinite range and the Boltzmann equation. Arch. Rational Mech. Anal. 77 (1981) 11-21. | MR 630119 | Zbl 0547.76085

[3] G. I. Barenblatt, Scaling, Self-similarity, and Intermediate Asymptotics. Cambridge Univ. Press, New York (1996). | MR 1426127 | Zbl 0907.76002

[4] D. Benedetto, E. Caglioti and M. Pulvirenti, A kinetic equation for granular media. RAIRO Modél. Math. Anal. Numér. 31 (1997) 615-641. | Numdam | MR 1471181 | Zbl 0888.73006

[5] D. Benedetto, E. Caglioti and M. Pulvirenti, Erratum : A kinetic equation for granular media [RAIRO Modél. Math. Anal. Numér. 31 (1997) 615-641]. ESAIM : M2AN 33 (1999) 439-441. | Numdam | MR 1471181 | Zbl 0888.73006

[6] C. Bizon, J. B. Shattuck, M. D. Swift, W. D. Mc Cormick and H. L. Swinney, Pattern in 2D vertically oscillated granular layers : simulation and experiments. Phys. Rev. Lett. 80 (1998) 57-60.

[7] A. V. Bobylev, J. A. Carillo and I. Gamba, On some properties of kinetic and hydrodynamics equations for inelastic interactions. J. Statist. Phys. 98 (2000) 743-773. | MR 1749231 | Zbl 1056.76071

[8] C. Cercignani, R. Illner and M. Pulvirenti, The mathematical theory of dilute gases. Springer Ser. Appl. Math. Sci. 106, Springer-Verlag, New York (1994). | MR 1307620 | Zbl 0813.76001

[9] L. Desvillettes, About the regularizing properties of the non-cut-off Kac equation. Comm. Math. Phys. 168 (1995) 417-440. | MR 1324404 | Zbl 0827.76081

[10] Y. Du, H. Li and L. P. Kadanoff, Breakdown of hydrodynamics in a one-dimensional system of inelastic particles. Phys. Rev. Lett. 74 (1995) 1268-1271.

[11] D. Goldman, M. D. Shattuck, C. Bizon, W. D. Mccormick, J. B. Swift and H. L. Swinney, Absence of inelastic collapse in a realistic three ball model. Phys. Rev. E 57 (1998) 4831-4833.

[12] I. Goldhirsch, Scales and kinetics of granular flows. Chaos 9 (1999) 659-672. | Zbl 1055.76569

[13] M. Kac, Probability and related topics in the physical sciences. New York (1959). | MR 102849 | Zbl 0087.33003

[14] L. Kantorovich, On translation of mass (in Russian). Dokl. AN SSSR 37 (1942) 227-229.

[15] L. Landau, Die kinetische Gleichung für den Fall Coulombscher Wechselwirkung. Phys. Z. Sowjet. 10 (1936) 154. Trad.: The transport equation in the case of Coulomb interactions, in Collected papers of L.D. Landau, D. ter Haar Ed., Pergamon Press, Oxford (1981) 163-170. | Zbl 0015.38202

[16] S. Mcnamara and W. R. Young, Inelastic collapse and clumping in a one-dimensional granular medium. Phys. Fluids A 4 (1992) 496-504.

[17] S. Mcnamara and W. R. Young, Kinetics of a one-dimensional granular medium in the quasi-elastic limit. Phys. Fluids A 5 (1993) 34-45. | MR 1196416

[18] G. Naldi, L. Pareschi and G. Toscani, Spectral methods for a singular Boltzmann equation for granular flows and numerical quasi elastic limit. Preprint (2000).

[19] G. Toscani, The grazing collision asymptotic of the non cut-off Kac equation. RAIRO Modél. Math. Anal. Numér. 32 (1998) 763-772. | Numdam | MR 1652617 | Zbl 0912.76081

[20] I. Vaida, Theory of statistical Inference and Information. Kluwer Academic Publishers, Dordrecht (1989). | Zbl 0711.62002

[21] L. N. Vasershtein, Markov processes on countable product space describing large systems of automata (in Russian). Problemy Peredachi Informatsii 5 (1969) 64-73. | MR 314115 | Zbl 0273.60054

[22] C. Villani, Contribution à l'étude mathématique des équations de Boltzmann et de Landau en théorie cinétique des gaz et des plasmas. Ph. D. thesis, Univ. Paris-Dauphine (1998).

[23] C. Villani, On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations. Arch. Rational Mech. Anal. 143 (1998) 273-307. | MR 1650006 | Zbl 0912.45011

[24] C. Villani, Contribution à l'étude mathématique des collisions en théorie cinétique. Ceremade, Paris IX-Dauphine, January 24 (2000).

[25] V. M. Zolotarev, Probability Metrics. Theory Probab. Appl. 28 (1983) 278-302. | Zbl 0533.60025