TY - JOUR
T1 - A minimal hyperbolic system for unstable shock waves
AU - Kabanov, Dmitry I.
AU - Kasimov, Aslan R.
N1 - KAUST Repository Item: Exported on 2021-02-09
Acknowledgements: Dmitry Kabanov was supported by KAUST
\nAslan Kasimov was supported by the Russian Foundation for Basic Research through grants #17-53-12018 and #17-01-00070
PY - 2018/11/6
Y1 - 2018/11/6
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.
UR - http://hdl.handle.net/10754/629732
UR - https://linkinghub.elsevier.com/retrieve/pii/S1007570418303381
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
VL - 70
SP - 282
EP - 301
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
SN - 1007-5704
ER -