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We establish one-dimensional spectral, or "normal modes", stability of ZNDdetonations in the small heat release limit and the related high overdrivelimit with heat release and activation energy held fixed, verifying numericalobservations of Erpenbeck in the 1960s. The key technical points are astrategic rescaling of parameters converting the infinite overdrive limit to afinite, regular perturbation problem, and a careful high-frequency analysisdepending uniformly on model parameters. The latter recovers the importantresult of high-frequency stability established by Erpenbeck by somewhatdifferent techniques. Notably, the techniques used here yield quantitativeestimates well suited for numerical stability investigation.

High-frequency asymptotics and 1-D stability of ZND detonations in the small-heat release and high-overdrive limits