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

top
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

top

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

top
  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. Cédric Villani, Hypocoercive Diffusion Operators
  4. Giovanni Naldi, Lorenzo Pareschi, Giuseppe Toscani, Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit
  5. G. Toscani, Funzionali entropia ed equilibrio di sistemi di molte particelle
  6. Adrien Blanchet, On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher
  7. Giovanni Naldi, Lorenzo Pareschi, Giuseppe Toscani, Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit
  8. Stefano Lisini, Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces
  9. François Bolley, Limite de champ moyen de systèmes de particules
  10. François Bolley, Arnaud Guillin, Florent Malrieu, Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.