### 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 language | English (US) |
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Pages (from-to) | 909-925 |

Number of pages | 17 |

Journal | Royal Society of Edinburgh - Proceedings A |

Volume | 131 |

Issue number | 6 |

State | Published - Dec 1 2001 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Jenssen, H. K., & Sinestrari, C. (2001). On the spreading of characteristics for non-convex conservation laws.

*Royal Society of Edinburgh - Proceedings A*,*131*(6), 909-925.