### Abstract

In this paper, we study the formation of finite time singularities in the form of super norm blowup for a spatially inhomogeneous hyperbolic system. The system is related to the variational wave equations as those in R. Glassey, J. Hunter, and Y. Zheng [J. Differential Equations, 129 (1996), pp. 49-78]. The system possesses a unique C^{1} solution before the emergence of vacuum in finite time, for given initial data that are smooth enough, bounded, and uniformly away from vacuum. At the occurrence of blowup, the density becomes zero, while the momentum stays finite; however, the velocity and the density of the energy are both infinity.

Original language | English (US) |
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Pages (from-to) | 758-785 |

Number of pages | 28 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 47 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2015 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Computational Mathematics
- Applied Mathematics

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## Cite this

Chen, G., Huang, T., & Liu, C. (2015). Finite time singularities for hyperbolic systems.

*SIAM Journal on Mathematical Analysis*,*47*(1), 758-785. https://doi.org/10.1137/140986359