# One-dimensional kinetic models of granular flows

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

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topToscani, 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 -

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## Citations in EuDML Documents

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

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