Finite time singularities for hyperbolic systems

Geng Chen, Tao Huang, Chun Liu

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 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.

Original languageEnglish (US)
Pages (from-to)758-785
Number of pages28
JournalSIAM Journal on Mathematical Analysis
Volume47
Issue number1
DOIs
StatePublished - Jan 1 2015

Fingerprint

Finite-time Singularities
Hyperbolic Systems
Blow-up
Vacuum
Variational Equation
Wave equations
Unique Solution
Wave equation
Momentum
Differential equations
Infinity
Differential equation
Norm
Zero
Energy
Form

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

Chen, Geng ; Huang, Tao ; Liu, Chun. / Finite time singularities for hyperbolic systems. In: SIAM Journal on Mathematical Analysis. 2015 ; Vol. 47, No. 1. pp. 758-785.
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Finite time singularities for hyperbolic systems. / Chen, Geng; Huang, Tao; Liu, Chun.

In: SIAM Journal on Mathematical Analysis, Vol. 47, No. 1, 01.01.2015, p. 758-785.

Research output: Contribution to journalArticle

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