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CONTRACTIVE METRICS FOR SCALAR CONSERVATION LAWS

Ecole normale supérieure de Lyon, Umpa, 46, allée d'Italie, F-69364 Lyon Cedex 07, France

Laboratoire J. A. Dieudonné, UMR CNRS 6621, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 2, France

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GRÉGOIRE LOEPER

Fields Institute & University of Toronto, Ecole Polytechnique Fédérale de Lausanne, SB-IMA, 10015 Lausanne, Canada

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https://doi.org/10.1142/S0219891605000397Cited by:19 (Source: Crossref)

Abstract

We consider non-decreasing entropy solutions to 1-d scalar conservation laws and show that the spatial derivatives of such solutions satisfy a contraction property with respect to the Wasserstein distance of any order. This result extends the L¹-contraction property shown by Kružkov.

Keywords:

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