Nonclassical Shocks and the Cauchy Problem for Nonconvex Conservation
D. Amadori, B. Baiti, P. G. LeFloch, and B. Piccoli
The Riemann problem for a conservation law with
a nonconvex (cubic) flux can be solved in a class
of admissible nonclassical solutions that may violate
the Oleinik entropy condition but satisfy a single
entropy inequality and a kinetic relation.
We use such a nonclassical Riemann solver in a front tracking
algorithm, and prove that the approximate solutions
remain bounded in the total variation norm.
The nonclassical shocks induce an increase of the total variation
and, therefore, the classical measure of total variation
must be modified accordingly. We prove that the front tracking
scheme converges strongly to a weak solution satisfying
the entropy inequality.
- Available as PostScript
- Nonclassical Shocks and the Cauchy Problem for Nonconvex Conservation
- D. Amadori,
- B. Baiti,
- P. G. LeFloch,
- B. Piccoli,
- Publishing information:
- Submitted by:
November 17 1997.
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