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Stability of Detonation Profiles in the ZND Limit

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Abstract

Confirming a conjecture of Lyng–Raoofi–Texier–Zumbrun, we show that stability of strong detonation waves in the ZND, or small-viscosity, limit is equivalent to stability of the limiting ZND detonation together with stability of the viscous profile associated with the component Neumann shock. Moreover, on bounded frequencies the nonstable eigenvalues of the viscous detonation wave converge to those of the limiting ZND detonation, while on frequencies of order one over viscosity, they converge to one over viscosity times those of the associated viscous Neumann shock. This yields immediately a number of examples of instability and Hopf bifurcation of reacting Navier–Stokes detonations through the extensive numerical studies of ZND stability in the detonation literature.

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  1. Indiana University, Bloomington, IN, 47405, USA

    Kevin Zumbrun

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  1. Kevin Zumbrun
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Correspondence to Kevin Zumbrun.

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Communicated by A. Bressan

Research of K. Zumbrun was partially supported under NSF grants no. DMS-0300487 and DMS-0801745.

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Zumbrun, K. Stability of Detonation Profiles in the ZND Limit. Arch Rational Mech Anal 200, 141–182 (2011). https://doi.org/10.1007/s00205-010-0342-6

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