Abstract
We construct a class of 3 × 3 systems of conservation laws with all characteristic fields genuinely nonlinear, and we show the existence of entropy solutions for these that blow up in sup-norm in finite time. The solutions are constructed by considering wave patterns where infinitely many shock waves are produced in finite time. We also consider the role of entropies as a mechanism for preventing this type of singular behavior.
Original language | English (US) |
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Pages (from-to) | 837-853 |
Number of pages | 17 |
Journal | Discrete and Continuous Dynamical Systems |
Volume | 7 |
Issue number | 4 |
State | Published - Dec 1 2001 |
All Science Journal Classification (ASJC) codes
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics