A minimal hyperbolic system for unstable shock waves

Dmitry I. Kabanov, Aslan R. Kasimov

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We present a computational analysis of a 2×2 hyperbolic system of balance laws whose solutions exhibit complex nonlinear behavior. Traveling-wave solutions of the system are shown to undergo a series of bifurcations as a parameter in the model is varied. Linear and nonlinear stability properties of the traveling waves are computed numerically using accurate shock-fitting methods. The model may be considered as a minimal hyperbolic system with chaotic solutions and can also serve as a stringent numerical test problem for systems of hyperbolic balance laws.
Original languageEnglish (US)
Pages (from-to)282-301
Number of pages20
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume70
DOIs
StatePublished - Nov 6 2018

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics
  • Numerical Analysis

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