A non-Maxwellian steady distribution for one-dimensional granular media

Journal of Statistical Physics

Volumn 91, Issue 5-6, 1998, Pages 979-990

  Benedetto, D ^a   Caglioti, E ^a   Carrillo, J A ^b   Pulvirenti, M ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF GRANADA   (Spain)

Author keywords

Fokker Planck; Granular media; Inelastic collisions; Kinetic equations

Indexed keywords

EID: 0032090818     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1023032000560     Document Type: Article

References (18)

1. A. Arnold, L. L. Bonilla, and P. A. Markowich, Liapunov functionals and large-time asymptotics of mean-field nonlinear Fokker-Planck equations, to appear on Transport Theory and Stat. Phys.
2. D. Benedetto and E. Caglioti, in preparation.
3. D. Benedetto, E. Caglioti, and M. Pulvirenti, A kinetic equation for granular media, Math. Mod. and Num. An. 31(5):615-641 (1997).
4. B. Bernu and R. Mazighi, One-dimensional bounce of inelastically colliding marbles on a wall, Jour. of Phys. A: Math. Gen. 23:5745-5754 (1990).
5. L. L. Bonilla, J. A. Carrillo, and J. Soler, Asymptotic behavior of an initial-boundary value problem for the Vlasov-Poisson-Fokker-Planck system, SIAM J. Appl. Math. 57: 1343-1372 (1997).
6. F. Bouchut and J. Dolbeault, On long asymptotics of the Vlasov-Fokker-Planck equation and of the Vlasov-Poisson-Fokker-Planck system with Coulombian and Newtonian potentials, Diff. and Integ. Equations 8:487-514 (1995).
7. S. Campbell, Rapid Granular Flows, Ann. Rev. of Fluid Mech. 22:57-92 (1990).
8. J. A. Carrillo, Global weak solutions for the initial-boundary value problems to the Vlasov-Poisson-Fokker-Planck system, to appear on Math. Meth. in the Appl. Sci.
9. P. Constantin, E. Grossman, and M. Mungan, Inelastic collisions of three particles on a line as a two-dimensional billiard, Physica D 83:409-420 (1995).
10. Y. Du, H. Li, and L. P. Kadanoff, Breakdown of hydrodynamics in a one-dimensional system of inelastic particles, Phys. Rev. Lett. 74(8):1268-1271 (1995).
11. S. E. Esipov and T. Pöschel, Boltzmann Equation and Granular Hydrodynamics, (preprint) (1995).
12. I. Goldhirsch and G. Zanetti, Clustering instability in dissipative gases, Phys. Rev. Lett. 70:1619-1622 (1993).
13. P. K. Haff, Grain flow as a fluid mechanic phenomenon, J. Fluid Mech. 134:401-430 (1983).
14. Mc Kean, Lectures in Diff. Eqs, A. K. Aziz, ed. Von Nostrand, Vol. II, (1964), p. 177.
15. S. Mac Namara and W. R. Young, Inelastic collapse and clumping in a one-dimensional granular medium, Phys. of Fluids A 4(3):496-504 (1992).
16. S. Mac Namara and W. R. Young, Kinetic of a one-dimensional granular in the quasi elastic limit medium, Phys. of Fluids A 5(1):34-45 (1993).
17. N. Sela and I. Goldhirsch, Hydrodynamics of a one-dimensional granular medium, Phys. of Fluids 7(3):34-45 (1995).
18. H. D. Victory and B. P. O'Dwyer, On classical solutions of Vlasov-Poisson-Fokker-Planck systems, Indiana Univ. Math. J. 39:105-157 (1990).