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One-dimensional kinetic models of granular flows

Published online by Cambridge University Press:  15 April 2002

Giuseppe Toscani
Giuseppe Toscani*
Affiliation:
Dipartimento di Matematica, Università di Pavia, 27100 Pavia, Italy. (toscani@dimat.unipv.it)
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Abstract

We introduce and discuss a one-dimensional kinetic model of the Boltzmann equation with dissipative collisions and variable coefficient of restitution. Then, the behavior of the Boltzmann equation in the quasi elastic limit is investigated for a wide range of the rate function. By this limit procedure we obtain a class of nonlinear equations classified as nonlinear friction equations. The analysis of the cooling process shows that the nonlinearity on the relative velocity is of paramount importance for the finite time extinction of the solution.

Keywords

Granular gasesBoltzmann equationlong-time behavior of solutions.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 6 , November 2000 , pp. 1277 - 1291
Copyright
© EDP Sciences, SMAI, 2000

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