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

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

    Research output: Contribution to journalArticleResearchpeer-review

    249 Citations (Scopus)

    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 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 [28].
    Original languageEnglish
    Pages (from-to)971-1018
    JournalRevista Matematica Iberoamericana
    Volume19
    Issue number3
    DOIs
    Publication statusPublished - 1 Jan 2003

    Keywords

    • Generalized log-Sobolev inequalities
    • Inelastic collision models
    • Rates of convergence
    • Wasserstein distance

    Fingerprint Dive into the research topics of 'Kinetic equilibration rates for granular media and related equations: Entropy dissipation and mass transportation estimates'. Together they form a unique fingerprint.

    Cite this