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GRADIENT DRIVEN AND SINGULAR FLUX BLOWUP OF SMOOTH SOLUTIONS TO HYPERBOLIC SYSTEMS OF CONSERVATION LAWS

HELGE KRISTIAN JENSSEN

Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA

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and

ROBIN YOUNG

Department of Mathematics, University of Massachusetts, Amherst, MA 01003, USA

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https://doi.org/10.1142/S021989160400024XCited by:8 (Source: Crossref)

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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