On the spreading of characteristics for non-convex conservation laws

Helge Kristian Jenssen, Carlo Sinestrari

Research output: Contribution to journalArticle

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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.

Original languageEnglish (US)
Pages (from-to)909-925
Number of pages17
JournalRoyal Society of Edinburgh - Proceedings A
Volume131
Issue number6
StatePublished - Dec 1 2001

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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