On the spreading of characteristics for non-convex conservation laws

Authors
Jenssen, HK Sinestrari, C
Citation
Hk. Jenssen et C. Sinestrari, On the spreading of characteristics for non-convex conservation laws, P RS EDIN A, 131, 2001, pp. 909-925
Citations number
16
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
ISSN journal
03082105 → ACNP
Volume
131
Year of publication
2001
Part
4
Pages
909 - 925
Database
ISI
SICI code
0308-2105(2001)131:<909:OTSOCF>2.0.ZU;2-E
Abstract
We study the spreading of characteristics for a class of one-dimensional sc alar conservation laws for which the flux function has one point of inflect ion. It is well known that in the convex case the characteristic speed sati sfies a one-sided Lipschitz estimate. Using Dafermos' theory of generalized characteristics, we show that the characteristic speed in the non-convex c ase satisfies an Holder estimate. In addition, we give a one-sided Lipschit z estimate with an error term given by the decrease of the total variation of the solution.