Contractivity of Wasserstein metrics and asymptotic profiles for scalar conservation laws

José A. Carrillo, Marco Di Francesco, Corrado Lattanzio

Research output: Contribution to journalArticleResearchpeer-review

7 Citations (Scopus)

Abstract

The aim of this paper is to analyze contractivity properties of Wasserstein-type metrics for one-dimensional scalar conservation laws with nonnegative, L∞ and compactly supported initial data and its implications on the long time asymptotics. The flux is assumed to be convex and without any growth condition at the zero state. We propose a time-parameterized family of functions as intermediate asymptotics and prove the solutions, after a time-depending scaling, converge toward this family in the d∞-Wasserstein metric. This asymptotic behavior relies on the aforementioned contraction property for conservation laws in the space of probability densities metrized with the d∞-Wasserstein distance. Finally, we also give asymptotic profiles for initial data whose distributional derivative is a probability measure. © 2006 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)425-458
JournalJournal of Differential Equations
Volume231
DOIs
Publication statusPublished - 15 Dec 2006

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