Online Publication Date2018-11-06
Print Publication Date2019-05
Permanent link to this recordhttp://hdl.handle.net/10754/629732
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AbstractWe 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.
SponsorsDmitry 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