TY - JOUR

T1 - On the spreading of characteristics for non-convex conservation laws

AU - Jenssen, Helge Kristian

AU - Sinestrari, Carlo

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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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U2 - 10.1017/s0308210500001189

DO - 10.1017/s0308210500001189

M3 - Article

AN - SCOPUS:23044530305

SN - 0308-2105

VL - 131

SP - 909

EP - 925

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

IS - 6

ER -