Instability of unburnt gas for a scalar nonconvex combustion model

The ignition solutions for the scalar nonconvex Chapman–Jouguet (CJ) combustion model are studied as the ignited perturbation vanishes. We let the perturbation vanish in the result of the interactions of the combustion waves and noncombustion waves, thereby obtaining that the unburnt gas is unstable when the binding energy is larger than a critical value. Furthermore, in the vanishing process, the transitions between deflagration and detonation waves are observed.