TY - JOUR

T1 - Finite time singularities for hyperbolic systems

AU - Chen, Geng

AU - Huang, Tao

AU - Liu, Chun

N1 - Publisher Copyright:
© 2015 Society for Industrial and Applied Mathematics.

PY - 2015

Y1 - 2015

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 -