Preprint 2001-006

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 33 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.

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Paolo Baiti <>
Helge Kristian Jenssen <>
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<> February 7 2001.

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