Decay of small planar perturbations on a strong steady detonation: A differential–difference equation for the shock

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Abstract
In the context of the author’s mathematical analog for reactive flow, the problem of the decay of small planar perturbations on a steady overdriven detonation wave is considered. For particular choices of the reaction rate, the analysis can be carried far enough to yield a simple differential–difference equation for the shock‐state history. Analysis of this equation gives the natural frequencies and decay rates of the system and allows one to identify a ‘‘feedback length.’’ A set of sample ‘‘input’’ (applied perturbation) and corresponding ‘‘output’’ (shock‐state history) signals is presented.

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