### 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 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Computational Mathematics
- Applied Mathematics

### Cite this

*SIAM Journal on Mathematical Analysis*,

*47*(1), 758-785. https://doi.org/10.1137/140986359

}

*SIAM Journal on Mathematical Analysis*, vol. 47, no. 1, pp. 758-785. https://doi.org/10.1137/140986359

**Finite time singularities for hyperbolic systems.** / Chen, Geng; Huang, Tao; Liu, Chun.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Finite time singularities for hyperbolic systems

AU - Chen, Geng

AU - Huang, Tao

AU - Liu, Chun

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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 C1 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.

AB - 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 C1 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.

UR - http://www.scopus.com/inward/record.url?scp=84923958759&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84923958759&partnerID=8YFLogxK

U2 - 10.1137/140986359

DO - 10.1137/140986359

M3 - Article

AN - SCOPUS:84923958759

VL - 47

SP - 758

EP - 785

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 1

ER -