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89464 |
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|a Faria, Luiz M.
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|a Massachusetts Institute of Technology. Department of Mathematics
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|a Rosales, Rodolfo R.
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|a Kasimov, Aslan R.
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|a Rosales, Rodolfo R.
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|a Study of a Model Equation in Detonation Theory
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|b Society for Industrial and Applied Mathematics,
|c 2014-09-12T16:50:28Z.
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|z Get fulltext
|u http://hdl.handle.net/1721.1/89464
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|a 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 $ u_{t}+\tfrac{1}{2}\left(u^{2}-uu\left(0^{-},t\right)\right)_{x}=f\left(x,u\left(0^{-},t\right)\right),\;x\le0,\; 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.
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|a National Science Foundation (U.S.) (Grant DMS-1115278)
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|a National Science Foundation (U.S.) (Grant DMS-1007967)
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|a National Institutes of Health (U.S.) (grant DMS-0907955)
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|a Article
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|t SIAM Journal on Applied Mathematics
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