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

• Autores: Robert J. McCann, José Antonio Carrillo, Cédric Villani
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 19, Nº 3, 2003, págs. 971-1018
• Idioma: inglés
• Títulos paralelos:
  • Velocidades de equilibrado cinético para medios granulares y ecuaciones relacionadas: estimaciones de disipación de entropía y transporte de masa.
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• Resumen

  • 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].