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

We establish one-dimensional spectral, or "normal modes", stability of ZND detonations in the small heat release limit and the related high overdrive limit with heat release and activation energy held fixed, verifying numerical observations of Erpenbeck in the 1960s. The key technical points are a strategic rescaling of parameters converting the infinite overdrive limit to a finite, regular perturbation problem, and a careful high-frequency analysis depending uniformly on model parameters. The latter recovers the important result of high-frequency stability established by Erpenbeck by somewhat different techniques. Notably, the techniques used here yield quantitative estimates well suited for numerical stability investigation.