Solution of the bbgky hierarchy of inelastically interacting particles and its asymptotic
Z. Artemychenko. 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.
%0 Book Section
%1 statphys23_0841
%A Artemychenko, Z.Y.
%B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics
%C Genova, Italy
%D 2007
%E Pietronero, Luciano
%E Loreto, Vittorio
%E Zapperi, Stefano
%K boltzmann-grad gases granular limit statphys23 topic-7
%T Solution of the bbgky hierarchy of inelastically interacting particles and its asymptotic
%U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=841
%X 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.
@incollection{statphys23_0841,
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.},
added-at = {2007-06-20T10:16:09.000+0200},
address = {Genova, Italy},
author = {Artemychenko, Z.Y.},
biburl = {https://www.bibsonomy.org/bibtex/2811f88abd14191b593dacd68395e4122/statphys23},
booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano},
interhash = {14745a689762d18cf861e7a87785130c},
intrahash = {811f88abd14191b593dacd68395e4122},
keywords = {boltzmann-grad gases granular limit statphys23 topic-7},
month = {9-13 July},
timestamp = {2007-06-20T10:16:30.000+0200},
title = {Solution of the bbgky hierarchy of inelastically interacting particles and its asymptotic},
url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=841},
year = 2007
}