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Transition to longitudinal instability of detonation waves is generically associated with Hopf bifurcation to time-periodic galloping solutions. (English) Zbl 1217.35138

The authors study the stability and Hopf bifurcation of viscous detonation waves of the active compressible Navier-Stokes equations in the one dimensional case, motivated by physical and numerical observations. By the pointwise semigroup techniques developed by themselves and others, the authors show rigorously that the transition to longitudinal instability of detonation waves is generically associated with Hopf bifurcation to time-periodic galloping solutions. This result completely agrees with the physical and numerical observations. Moreover, the authors establish the first full nonlinear stability results for strong detonations of the reactive compressible Navier-Stokes equations, which extends the previous results.
Reviewer: Cheng He (Beijing)

MSC:

35Q30 Navier-Stokes equations
76N15 Gas dynamics (general theory)
35B32 Bifurcations in context of PDEs
35B35 Stability in context of PDEs
76E19 Compressibility effects in hydrodynamic stability
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