TY - JOUR

T1 - Study of a Model Equation in Detonation Theory

AU - Faria, Luiz

AU - Kasimov, Aslan R.

AU - Rosales, Rodolfo R.

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2014/4/24

Y1 - 2014/4/24

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/555743

UR - http://epubs.siam.org/doi/abs/10.1137/130938232

UR - http://www.scopus.com/inward/record.url?scp=84903991094&partnerID=8YFLogxK

U2 - 10.1137/130938232

DO - 10.1137/130938232

M3 - Article

VL - 74

SP - 547

EP - 570

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 2

ER -