CONTRACTIVE METRICS FOR SCALAR CONSERVATION LAWS

Francois Bolley, Yann Brenier, Gregoire Loeper

Research output: Contribution to journalArticleResearchpeer-review

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 Kruzkov.
Original languageEnglish
Pages (from-to)91-107
Number of pages17
JournalJournal of Hyperbolic Differential Equations
Volume2
Issue number1
Publication statusPublished - 2005
Externally publishedYes

Keywords

  • Conservation laws
  • entropy solutions
  • Wasserstein distance

Cite this

Bolley, Francois ; Brenier, Yann ; Loeper, Gregoire. / CONTRACTIVE METRICS FOR SCALAR CONSERVATION LAWS. In: Journal of Hyperbolic Differential Equations. 2005 ; Vol. 2, No. 1. pp. 91-107.
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CONTRACTIVE METRICS FOR SCALAR CONSERVATION LAWS. / Bolley, Francois; Brenier, Yann; Loeper, Gregoire.

In: Journal of Hyperbolic Differential Equations, Vol. 2, No. 1, 2005, p. 91-107.

Research output: Contribution to journalArticleResearchpeer-review

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T1 - CONTRACTIVE METRICS FOR SCALAR CONSERVATION LAWS

AU - Bolley, Francois

AU - Brenier, Yann

AU - Loeper, Gregoire

PY - 2005

Y1 - 2005

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AB - 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 Kruzkov.

KW - Conservation laws

KW - entropy solutions

KW - Wasserstein distance

UR - http://www.worldscientific.com/doi/pdf/10.1142/S0219891605000397

M3 - Article

VL - 2

SP - 91

EP - 107

JO - Journal of Hyperbolic Differential Equations

JF - Journal of Hyperbolic Differential Equations

SN - 0219-8916

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