A minimal hyperbolic system for unstable shock waves

Dmitry I. Kabanov; Aslan R. Kasimov

doi:10.1016/j.cnsns.2018.10.022

A minimal hyperbolic system for unstable shock waves

Dmitry I. Kabanov, Aslan R. Kasimov^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 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 language	English (US)
Pages (from-to)	282-301
Number of pages	20
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	70
DOIs	https://doi.org/10.1016/j.cnsns.2018.10.022
State	Published - May 2019
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2018

Keywords

Bifurcations
Chaos
Detonation
Hyperbolic systems
Shock waves
Stability

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Applied Mathematics

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10.1016/j.cnsns.2018.10.022

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AU - Kabanov, Dmitry I.

AU - Kasimov, Aslan R.

PY - 2019/5

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AB - 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.

KW - Bifurcations

KW - Chaos

KW - Detonation

KW - Hyperbolic systems

KW - Shock waves

KW - Stability

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VL - 70

SP - 282

EP - 301

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

ER -

A minimal hyperbolic system for unstable shock waves

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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