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)|
|Number of pages||17|
|Journal||Royal Society of Edinburgh - Proceedings A|
|State||Published - Dec 1 2001|
All Science Journal Classification (ASJC) codes