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On the spreading of characteristics for non-convex conservation laws

Published online by Cambridge University Press:  12 July 2007

Helge Kristian Jenssen  and
Carlo Sinestrari
Helge Kristian Jenssen
Affiliation:
SISSA, Via Beirut 2–4, 34014 Trieste, Italy (jenssen@sissa.it)
Carlo Sinestrari
Affiliation:
Università di Roma ‘Tor Vergata’, Via della Ricerca Scientifica, 00133 Roma, Italy (sinestra@mat.uniroma2.it)
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Abstract

We study the spreading of characteristics for a class of one-dimensional scalar conservation laws for which the flux function has one point of inflection. It is well known that in the convex case the characteristic speed satisfies a one-sided Lipschitz estimate. Using Dafermos' theory of generalized characteristics, we show that the characteristic speed in the non-convex case satisfies an Hölder estimate. In addition, we give a one-sided Lipschitz estimate with an error term given by the decrease of the total variation of the solution.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 4 , August 2001 , pp. 909 - 925
Copyright
Copyright © Royal Society of Edinburgh 2001

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