Preprint 2004-012

Gradient Driven and Singular Flux Blowup of Smooth Solutions to Hyperbolic Conservation Laws

Helge Kristian Jenssen and Robin Young

Abstract: We consider two new classes of examples of sup-norm blowup in finite time for strictly hyperbolic systems of conservation laws. The explosive growth in amplitude is caused either by a gradient catastrophe or by a singularity in the flux function. The examples show that solutions of (uniformly) strictly hyperbolic systems can remain as smooth as the initial data until the time of blowup. Consequently, blowup in amplitude is not necessarily strictly preceded by shock formation.

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Helge Kristian Jenssen, <>
Robin Young, <>
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<> March 28 2004.

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