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Contractive metrics for scalar conservation laws

F. Bolley·Y. Brenier·G. Loeper
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Abstract

We consider nondecreasing 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 L^1-contraction property shown by Kruzkov.

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F. Bolley, Y. Brenier, G. Loeper. 2005-04-07. Contractive metrics for scalar conservation laws. https://arxiv.org/abs/math/0504136

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