Blowup with Small BV Data in Hyperbolic Conservation Laws

Document Type

Article

Department or Administrative Unit

Geological Sciences

Publication Date

1-2006

Abstract

We construct weak solutions of 3×3 conservation laws which blow up in finite time. The system is strictly hyperbolic at every state in the solution, and the data can be chosen to have arbitrarily small total variation. This is thus an example where Glimm's existence theorem fails to apply, and it implies the necessity of uniform hyperbolicity in Glimm's theorem. Because our system is very simple, we can carry out explicit calculations and understand the global geometry of wave curves.

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The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-005-0370-9

Journal

Archive for Rational Mechanics and Analysis

Rights

Copyright © 2006 Springer International Publishing

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