Contractions in the 2-Wasserstein length space and thermalization of granular media

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

Research output: Contribution to journalArticleResearchpeer-review

177 Citations (Scopus)

Abstract

An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by reformulating the dynamical problem as the gradient flow of a convex energy on an infinite-dimensional manifold. An abstract theory is developed for gradient flows in length spaces, which shows how degenerate convexity (or even non-convexity) - if uniformly controlled - will quantify contractivity (limit expansivity) of the flow.
Original languageEnglish
Pages (from-to)217-263
JournalArchive for Rational Mechanics and Analysis
Volume179
DOIs
Publication statusPublished - 1 Jan 2006

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