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

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

doi:https://doi.org/10.1007/s00205-005-0386-1

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

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

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

218 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 language	English
Pages (from-to)	217-263
Journal	Archive for Rational Mechanics and Analysis
Volume	179
DOIs	https://doi.org/10.1007/s00205-005-0386-1
Publication status	Published - 1 Jan 2006

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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.",

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AB - 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.

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VL - 179

SP - 217

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JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

ER -

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

Abstract

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