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 -