On the spreading of characteristics for non-convex conservation laws

Helge Kristian Jenssen; Carlo Sinestrari

doi:10.1017/S0308210500001189

Abstract

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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.

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On the spreading of characteristics for non-convex conservation laws

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