Blowup in L for a class of genuinely nonlinear hyperbolic systems of conservation laws

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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 languageEnglish (US)
Pages (from-to)837-853
Number of pages17
JournalDiscrete and Continuous Dynamical Systems
Volume7
Issue number4
StatePublished - Dec 1 2001

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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