Publication Date
2006
Journal or Book Title
Archive for Rational Mechanics and Analysis
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.
DOI
https://doi.org/10.1007/s00205-005-0370-9
Pages
31-54
Volume
179
Issue
1
Recommended Citation
Young, Robin and Szeliga, Walter, "Blowup with small BV data in hyperbolic conservation laws" (2006). Archive for Rational Mechanics and Analysis. 1010.
https://doi.org/10.1007/s00205-005-0370-9