Preprint 2000-024

On the Spreading of Characteristics for Nonconvex Conservation Laws

Helge Kristian Jenssen and Carlo Sinestrari

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 nonconvex case satisfies a H\"{o}lder 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.

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Helge Kristian Jenssen, <>
Carlo Sinestrari, <>
Publishing information:
This is an expanded version of preprint 1998-023.
Submitted by:
<> June 8 2000.

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