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Ukrainian Mathematical Journal

, Volume 57, Issue 6, pp 967–990 | Cite as

Analog of the Liouville Equation and BBGKY Hierarchy for a System of Hard Spheres with Inelastic Collisions

  • D. Ya. Petrina
  • G. L. Caraffini
Article

Abstract

Dynamics of a system of hard spheres with inelastic collisions is investigated. This system is a model for granular flow. The map induced by a shift along the trajectory does not preserve the volume of the phase space, and the corresponding Jacobian is different from one. A special distribution function is defined as the product of the usual distribution function and the squared Jacobian. For this distribution function, the Liouville equation with boundary condition is derived. A sequence of correlation functions is defined for canonical and grand canonical ensemble. The generalized BBGKY hierarchy and boundary condition are deduced for correlation functions.

Keywords

Boundary Condition Distribution Function Correlation Function Phase Space Hard Sphere 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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REFERENCES

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    D. Ya. Petrina, V. I. Gerasimenko, and P. V. Malyshev, Mathematical Foundations of Classical Statistical Mechanics. Continuous Systems, Taylor and Francis, London (2002).Google Scholar
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    C. Cercignani, V. I. Gerasimenko, and D. Ya. Petrina, Many-Particle Dynamics and Kinetic Equations, Kluwer, Dordrecht (1998).Google Scholar
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    C. Cercignani, Theory and Application of the Boltzmann Equation, Scottish Academic Press, Edinburgh (1975).Google Scholar
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    D. Benedetto, E. Caglioti, and M. Pulvirenti, “A kinetic equation for granular media,” Math. Model. Numer. Anal., 33, No.2, 439–441 (1999).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • D. Ya. Petrina
    • 1
  • G. L. Caraffini
    • 2
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKyivUkraine
  2. 2.University of ParmaParmaItaly

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