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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
60/2003

Minimal entropy conditions for Burgers equation

Camillo De Lellis, Felix Otto and Michael Westdickenberg

Abstract

We consider strictly convex, 1-d scalar conservation laws. We show that a single strictly convex entropy is sufficient to characterize a Kruzhkov solution. The proof uses the concept of viscosity solution for the related Hamilton-Jacobi equation.

Received:
10.07.03
Published:
10.07.03
MSC Codes:
35L65, 35L67
Keywords:
entropy solutions, entropy conditions, viscosity solutions

Related publications

inJournal
2004 Repository Open Access
Camillo De Lellis, Felix Otto and Michael Westdickenberg

Minimal entropy conditions for Burgers equation

In: Quarterly of applied mathematics, 62 (2004) 4, pp. 687-700