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


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.


Boundary Condition Distribution Function Correlation Function Phase Space Hard Sphere 
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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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