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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
9/2015

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

Elias Esselborn, Nicola Gigli and Felix Otto

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.

Received:
11.02.15
Published:
25.02.15
MSC Codes:
35L65
Keywords:
Burgers' equation, entropy solution, gradient flow, Wasserstein distance

Related publications

inJournal
2015 Repository Open Access
Elias Esselborn, Nicola Gigli and Felix Otto

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

In: Journal of mathematical analysis and applications, 435 (2015) 2, pp. 1525-1551