One dimensional stability of detonation waves

We prove two results about the stability of one dimensional detonation waves. Motivated by the similarities between strong detonation waves and Lax shocks, we apply Evans function theory developed to study the stability of shock waves to the more complicated setting of combustion. The first result is the calculation and evaluation of a stability index for strong detonations. The sign of this quantity provides a necessary condition for spectral stability. We find that for an ideal gas in the ZND limit, the index is consistent with stability. Moreover, we also include the calculation of stability indexes for both isentropic and full gas dynamics. The second result is that small amplitude strong detonation waves are stable in the limit of small heat release.