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

Keywords

Bifurcations
Chaos
Detonation
Hyperbolic systems
Shock waves
Stability

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Applied Mathematics

Access to Document

10.1016/j.cnsns.2018.10.022

Cite this

@article{fbafdb00c50f4a0f9cacdc5c5bf20cb7,

title = "A minimal hyperbolic system for unstable shock waves",

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.",

keywords = "Bifurcations, Chaos, Detonation, Hyperbolic systems, Shock waves, Stability",

author = "Kabanov, {Dmitry I.} and Kasimov, {Aslan R.}",

note = "Publisher Copyright: {\textcopyright} 2018",

year = "2019",

month = may,

doi = "10.1016/j.cnsns.2018.10.022",

language = "English (US)",

volume = "70",

pages = "282--301",

journal = "Communications in Nonlinear Science and Numerical Simulation",

issn = "1007-5704",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - A minimal hyperbolic system for unstable shock waves

AU - Kabanov, Dmitry I.

AU - Kasimov, Aslan R.

PY - 2019/5

Y1 - 2019/5

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=85056215674&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2018.10.022

DO - 10.1016/j.cnsns.2018.10.022

M3 - Article

AN - SCOPUS:85056215674

SN - 1007-5704

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

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this