Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates.

José A. Carrillo; Robert J. McCann; Cédric Villani

Revista Matemática Iberoamericana (2003)

  • Volume: 19, Issue: 3, page 971-1018
  • ISSN: 0213-2230

Abstract

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The long-time asymptotics of certain nonlinear , nonlocal, diffusive equations with a gradient flow structure are analyzed. In particular, a result of Benedetto, Caglioti, Carrillo and Pulvirenti [4] guaranteeing eventual relaxation to equilibrium velocities in a spatially homogencous model of granular flow is extended and quantified by computing explicit relaxation rates. Our arguments rely on establishing generalizations of logarithmic Sobolev inequalities and mass transportation inequalities, via either the Bakry-Emery method or the abstract approach of Otto and Villani [28].

How to cite

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Carrillo, José A., McCann, Robert J., and Villani, Cédric. "Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates.." Revista Matemática Iberoamericana 19.3 (2003): 971-1018. <http://eudml.org/doc/39703>.

@article{Carrillo2003,
abstract = {The long-time asymptotics of certain nonlinear , nonlocal, diffusive equations with a gradient flow structure are analyzed. In particular, a result of Benedetto, Caglioti, Carrillo and Pulvirenti [4] guaranteeing eventual relaxation to equilibrium velocities in a spatially homogencous model of granular flow is extended and quantified by computing explicit relaxation rates. Our arguments rely on establishing generalizations of logarithmic Sobolev inequalities and mass transportation inequalities, via either the Bakry-Emery method or the abstract approach of Otto and Villani [28].},
author = {Carrillo, José A., McCann, Robert J., Villani, Cédric},
journal = {Revista Matemática Iberoamericana},
keywords = {Ecuación de difusión; Ecuaciones parabólicas; Comportamiento asintótico; convergence to equilibrium; generalized log-Sobolev inequalities; Wasserstein distance; granular media equation; Bakry and Emery method; HWI method},
language = {eng},
number = {3},
pages = {971-1018},
title = {Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates.},
url = {http://eudml.org/doc/39703},
volume = {19},
year = {2003},
}

TY - JOUR
AU - Carrillo, José A.
AU - McCann, Robert J.
AU - Villani, Cédric
TI - Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates.
JO - Revista Matemática Iberoamericana
PY - 2003
VL - 19
IS - 3
SP - 971
EP - 1018
AB - The long-time asymptotics of certain nonlinear , nonlocal, diffusive equations with a gradient flow structure are analyzed. In particular, a result of Benedetto, Caglioti, Carrillo and Pulvirenti [4] guaranteeing eventual relaxation to equilibrium velocities in a spatially homogencous model of granular flow is extended and quantified by computing explicit relaxation rates. Our arguments rely on establishing generalizations of logarithmic Sobolev inequalities and mass transportation inequalities, via either the Bakry-Emery method or the abstract approach of Otto and Villani [28].
LA - eng
KW - Ecuación de difusión; Ecuaciones parabólicas; Comportamiento asintótico; convergence to equilibrium; generalized log-Sobolev inequalities; Wasserstein distance; granular media equation; Bakry and Emery method; HWI method
UR - http://eudml.org/doc/39703
ER -

Citations in EuDML Documents

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  1. Amarjit Budhiraja, Pierre Del Moral, Sylvain Rubenthaler, Discrete time markovian agents interacting through a potential
  2. Stefano Lisini, Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces
  3. Stefano Lisini, Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces
  4. Giovanni Naldi, Lorenzo Pareschi, Giuseppe Toscani, Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit
  5. Giovanni Naldi, Lorenzo Pareschi, Giuseppe Toscani, Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit
  6. Adrien Blanchet, On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher
  7. François Bolley, Arnaud Guillin, Florent Malrieu, Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation
  8. François Bolley, Limite de champ moyen de systèmes de particules

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