### Blowup in $L^{\infty}$ for a Class of Genuinely Nonlinear Hyperbolic Systems of Conservation Laws

Paolo Baiti and Helge Kristian Jenssen

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.

Paper:
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Author(s):
Paolo Baiti <baiti@dimi.uniud.it>
Helge Kristian Jenssen <kjenssen@indiana.edu>
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