Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
Carrillo, José A. ; McCann, Robert J. ; Villani, Cédric
Rev. Mat. Iberoamericana, Tome 19 (2003) no. 2, p. 971-1018 / Harvested from Project Euclid
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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 [BCCP98] guaranteeing eventual relaxation to equilibrium velocities in a spatially homogeneous 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 [OV00].
Publié le : 2003-12-14
Classification:  rates of convergence,  generalized log-Sobolev inequalities,  Wasserstein distance,  inelastic collision models,  35B40,  35K55,  35K65,  35Q72 
@article{1077293812,
     author = {Carrillo, Jos\'e A. and McCann, Robert J. and Villani, C\'edric},
     title = {Kinetic equilibration rates for granular media and related
equations: entropy dissipation and mass transportation estimates},
     journal = {Rev. Mat. Iberoamericana},
     volume = {19},
     number = {2},
     year = {2003},
     pages = { 971-1018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1077293812}
}

Carrillo, José A.; McCann, Robert J.; Villani, Cédric. Kinetic equilibration rates for granular media and related
equations: entropy dissipation and mass transportation estimates. Rev. Mat. Iberoamericana, Tome 19 (2003) no. 2, pp.  971-1018. http://gdmltest.u-ga.fr/item/1077293812/