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arXiv · 1807.05403

A minimal hyperbolic system for unstable shock waves

Dmitry I. Kabanov·Aslan R. Kasimov
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Abstract

We present a computational analysis of a 2$\times$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.

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Dmitry I. Kabanov, Aslan R. Kasimov. 2018-07-14. A minimal hyperbolic system for unstable shock waves. https://doi.org/10.1016/j.cnsns.2018.10.022

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