Algebraic contraction rate for distance between entropy solutions of scalar conservation laws

Elias Esselborn, Nicola Gigli, and Felix Otto

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Submission date: 11. Feb. 2015
Pages: 29
published in: Journal of mathematical analysis and applications, 435 (2015) 2, p. 1525-1551 
DOI number (of the published article): 10.1016/j.jmaa.2015.11.027
Bibtex
MSC-Numbers: 35L65
Keywords and phrases: Burgers' equation, entropy solution, gradient flow, Wasserstein distance
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Abstract:
We establish an algebraic contraction rate in a modified Wasserstein distance for solutions of scalar conservation laws with uniformly convex flux. We also show that our estimate is optimal w.r.t. scaling in time and discuss why it gives non-trivial information in relation to the stability of the rarefaction wave.