Abstract
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.
Original language | English (US) |
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Pages (from-to) | 345-372 |
Number of pages | 28 |
Journal | Journal of Differential Equations |
Volume | 151 |
Issue number | 2 |
DOIs | |
State | Published - Jan 20 1999 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
Keywords
- Conservation law
- Entropy
- Nonclassical shock
- Weak solution