Study of a Model Equation in Detonation Theory

Luiz Faria, Aslan R. Kasimov, Rodolfo R. Rosales

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14 Scopus citations


Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Model for shock wave chaos, Phys. Rev. Lett., 110 (2013), 104104]. The equation is ut+ 1/2 (u2-uu (0-, t))x=f (x, u (0-, t)), x > 0, t < 0. It describes a detonation shock at x = 0 with the reaction zone in x > 0. We investigate the nature of the steady-state solutions of this nonlocal hyperbolic balance law, the linear stability of these solutions, and the nonlinear dynamics. We establish the existence of instability followed by a cascade of period-doubling bifurcations leading to chaos. © 2014 Society for Industrial and Applied Mathematics.
Original languageEnglish (US)
Pages (from-to)547-570
Number of pages24
JournalSIAM Journal on Applied Mathematics
Issue number2
StatePublished - Apr 24 2014


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