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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 627-641 |
| Number of pages | 15 |
| Journal | Journal of Hyperbolic Differential Equations |
| Volume | 1 |
| Issue number | 4 |
| DOIs | |
| State | Published - Dec 1 2004 |
All Science Journal Classification (ASJC) codes
- Analysis
- General Mathematics