Benedetto, D.; Caglioti, E.; Pulvirenti, M. A kinetic equation for granular media. (English) Zbl 0888.73006 RAIRO, Modélisation Math. Anal. Numér. 31, No. 5, 615-641 (1997). Summary: We introduce and analyze a kinetic equation for a system of particles in one dimension performing inelastic collisions. Such a system has been proposed as a microscopic model for granular media. Cited in 3 ReviewsCited in 77 Documents MSC: 74A99 Generalities, axiomatics, foundations of continuum mechanics of solids 82B21 Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics Keywords:one-particle probability density; existence; uniqueness; asymptotic behavior; system of particles in one dimension; inelastic collisions; microscopic model for granular media PDFBibTeX XMLCite \textit{D. Benedetto} et al., RAIRO, Modélisation Math. Anal. Numér. 31, No. 5, 615--641 (1997; Zbl 0888.73006) Full Text: DOI EuDML References: [1] S. Mac NAMARA and W. R. YOUNG, 1992, Inelastic collapse and clumping in a one-dimensional granular medium, Phys. of Fluids, A4 (3), pp.496-504. [2] B. BERNU and MAZIGHI, 1990, One-dimensional bunce of inelastically colliding marbles on a wall, Jour, of Phys. A : Math. Gen., 23, pp. 5745-5754. Zbl0729.73648 · Zbl 0729.73648 [3] P. CONSTANTIN, E. GROSSMAN, M. MUNGAN, 1995, Inelastic collisions of three particles on a line as a two-dimensional billiard, Physica, D83, pp. 409-420. Zbl0900.70198 MR1334530 · Zbl 0900.70198 [4] I. GOLDHIRSCH, G. ZANETTI, 1993, Clustering Instability in Dissipative Gases, Phys. Rev. Lett., 70, pp. 1619-1622. [5] S. E. ESIPOV, T. PÖSCHEL, 1995, Boltzmann Equation and Granular Hydrodynamics (preprint). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.