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.
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U2 - 10.1137/140986359
DO - 10.1137/140986359
M3 - Article
AN - SCOPUS:84923958759
SN - 0036-1410
VL - 47
SP - 758
EP - 785
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
IS - 1
ER -