Kinetic and hydrodynamic models of nearly elastic granular flows

Monatshefte fur Mathematik

Volumn 142, Issue 1-2, 2004, Pages 179-192

  Toscani, Giuseppe ^a  

^a UNIVERSITY OF PAVIA   (Italy)

Author keywords

Granular gases; Long time behavior of solutions; Nonlinear friction equations

Indexed keywords

EID: 3042573547     PISSN: 00269255     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00605-004-0241-8     Document Type: Conference Paper

References (26)

1. Bellomo N, Esteban M, Lachowitz M (1995) Nonlinear kinetic equations with dissipative collisions. Appl Math Letters 8: 46-52
2. Benedetto D, Caglioti E, Pulvirenti M (1997) A kinetic equation for granular media. Mat Mod Numer Anal 31: 615-641
3. Benedetto D, Caglioti E, Carrillo JA, Pulvirenti M (1998) A non maxwellian distribution for onedimensional granular media. J Statist Phys 91: 979-990
4. Benedetto D, Caglioti E, Golse F, Pulvirenti M (2002) A hydrodynamic model arising in the context of granular media. Comput Math Appl (in press)
5. Bobylev AV, Carrillo J-A, Gamba I (2000) On some properties of kinetic and hydrodynamics equations for inelastic interactions. J Statist Phys 98: 743-773
6. Brey JJ, Dufty JW, Santos A (1997) Dissipative dynamics for hard spheres. J Statist Phys 87: 1051-1068
7. Brilliantov NV, Pöschel T (2000) Granular gases with impact-velocity dependent restitution coefficient. In: Pöschel T, Luding S (eds) Granular Gases. Lect Notes Physics 564: 100-124. Berlin Heidelberg New York: Springer
8. Brilliantov NV, Pöschel T (2000) Granular gases - the early stage. In: Reguera D et al (eds) Coherent Structures in Classical Systems. Lect Notes Phys 567:408-419. Berlin Heidelberg New York: Springer
9. Carrillo JA, Cercignani C, Gamba IM (2000) Steady states of a Boltzmann equation for driven granular media. Phys Rev E (3) 62: 7700-7707
10. Carrillo JA, McCann RJ, Villani C (2003) Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates. Revista Mat Iberoamericana 19: 1-48
11. Cercignani C, Illner R, Pulvirenti M (1994) The Mathematical Theory of Dilute Gases. Berlin Heidelberg New York: Springer
12. Cercignani C (1995) Recent developments in the mechanism of granular materials. Fisica Matematica e ingegneria delle strutture. Bologna: Pitagora Editrice
13. Du Y, Li H, Kadanoff LP (1995) Breakdown of hydrodynamics in a one-dimensional system of inelastic particles. Phys Rev Lett 74: 1268-1271
14. Esipov S, Pöschei T (1997) The granular phase diagram. J Stat Phys 86: 1385-1395
15. Fréchet M (1951) Sur les tableaux de corrélation dont les marges sont données. Ann Univ Lyon Sect A 14: 53-77
16. Goldman D, Shattuck MD, Bizon C, McCormick WD, Swift JB, Swinney HL (1998) Absence of inelastic collapse in a realistic three ball model. Phys Rev E 57: 4831-4833
17. Goldhirsch I (1990) Scales and kinetics of granular flows. Chaos 9: 659-672
18. Hailiang Li, Toscani G (2004) Long-time asymptotics of kinetic models of granular flows. Arch Rational Mech Anal (to appear)
19. Jenkins JT, Richman MW (1985) Grad's 13-moment system for a dense gas of inelastic spheres. Arch Rational Mech Anal 87: 355-377
20. McNamara S, Young WR (1992) Inelastic collapse and clumping in a one-dimensional granular medium. Phys Fluids A 4: 496-504
21. McNamara S, Young WR (1993) Kinetics of a one-dimensional granular medium in the quasielastic limit. Phys Fluids A 5: 34-45
22. Naldi G, Pareschi L, Toscani G (2003) Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit. RAIRO Model Math Anal Nurner 37: 73-90
23. Ramírez R, Pöschei T, Brilliantov NV, Schwager T (1999) Coefficient of restitution of colliding viscoelastic spheres. Phys Rev E 60: 4465-4472
24. Toscani G (2000) One-dimensional kinetic models of granular flows. RAIRO Modél Math Anal Numér 34: 1277-1292
25. Toscani G, Villani C (1999) Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation. Commun Math Phys 203: 667-706
26. Vasershtein LN (1969) Markov processes on countable product space describing large systems of automata (in Russian). Probl Pered Inform 5: 64-73