Nonlinear Stability of Weak Detonation Waves¶for a Combustion Model

Abstract:

We show that the weak detonation waves for a combustion model of Rosales–Majda are nonlinearly stable. Because of the strongly nonlinear nature of the wave, usual stability analysis of weakly nonlinear nature does not apply. The chemical switch on-off is the main feature of nonlinearity. In particular, the propagation of the wave depends sensitively on the tail behaviour of the flow in front of it. Unlike the strong detonation waves, a weak detonation is supersonic and there is the separation of the gas waves from the reacting front. As a consequence, the reacting front needs to be traced.