One-dimensional kinetic models of granular flows

Giuseppe Toscani

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 6, page 1277-1291
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Toscani, Giuseppe. "One-dimensional kinetic models of granular flows." ESAIM: Mathematical Modelling and Numerical Analysis 34.6 (2010): 1277-1291. <http://eudml.org/doc/197486>.

@article{Toscani2010,
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. },
author = {Toscani, Giuseppe},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Granular gases; Boltzmann equation; long-time behavior of solutions.; granular flows; one-dimensional kinetic model; dissipative collisions; variable coefficient of restitution; quasi-elastic limit; nonlinear friction},
language = {eng},
month = {3},
number = {6},
pages = {1277-1291},
publisher = {EDP Sciences},
title = {One-dimensional kinetic models of granular flows},
url = {http://eudml.org/doc/197486},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Toscani, Giuseppe
TI - One-dimensional kinetic models of granular flows
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 6
SP - 1277
EP - 1291
AB - 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.
LA - eng
KW - Granular gases; Boltzmann equation; long-time behavior of solutions.; granular flows; one-dimensional kinetic model; dissipative collisions; variable coefficient of restitution; quasi-elastic limit; nonlinear friction
UR - http://eudml.org/doc/197486
ER -

References

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Citations in EuDML Documents

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  1. Giovanni Naldi, Lorenzo Pareschi, Giuseppe Toscani, Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit
  2. Giovanni Naldi, Lorenzo Pareschi, Giuseppe Toscani, Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit
  3. Dario Benedetto, Mario Pulvirenti, On the one-dimensional Boltzmann equation for granular flows
  4. Dario Benedetto, Mario Pulvirenti, On the one-dimensional Boltzmann equation for granular flows

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