Incollection,
Solution of the bbgky hierarchy of inelastically interacting particles and its asymptotic
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
Many recent papers consider the Boltzmann-type and
Boltzmann-Enskog-type equations for inelastically interacting
particles as original evolution equations. We develop the approach
based on the dynamics of many inelastically colliding particles. As
a result we are able to justify properly the kinetic equations which
previous works have already applied a priori to the description of
granular gases.
The dissipative character of the interaction between grains leads
to some non-trivial features from mathematical point of view in the
description of the corresponding dynamical system. For example, the
trivial dynamics (free motion) in the Boltzmann-Grad limit for
elastically interacting one-dimensional hard spheres, and nontrivial
dynamics in a limit of inelastic interaction. We prove the
Boltzmann-Grad limit theorem for the solutions of BBGKY hierarchy of
such system.
1. C.Cercignani,
V.Gerasimenko and D.Petrina. Many-Particle Dynamics and Kinetic
Equations Dordrecht: Kluwer Acad./Plenum Publ. 1997, 252p.
