Preprint 2000-024
On the Spreading of Characteristics for Nonconvex Conservation Laws
Helge Kristian Jenssen and Carlo Sinestrari
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 nonconvex case satisfies a H\"{o}lder 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.
- Paper:
- Available as PostScript (292 Kbytes) or
gzipped PostScript (112 Kbytes; uncompress
using gunzip).
- Author(s):
- Helge Kristian Jenssen,
<jenssen@sissa.it>
- Carlo Sinestrari,
<sinestra@mat.uniroma2.it>
- Publishing information:
-
- Comments:
- This is an expanded version of preprint
1998-023.
- Submitted by:
-
<jenssen@sissa.it>
June 8 2000.
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