Archive for Rational Mechanics and Analysis

, Volume 179, Issue 1, pp 31–54

Blowup with Small BV Data in Hyperbolic Conservation Laws

Authors

    • Department of Mathematics & StatisticsUniversity of Massachusetts
  • Walter Szeliga
    • Department of Mathematics & StatisticsUniversity of Massachusetts
Article

DOI: 10.1007/s00205-005-0370-9

Cite this article as:
Young, R. & Szeliga, W. Arch. Rational Mech. Anal. (2006) 179: 31. doi:10.1007/s00205-005-0370-9

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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2005