Nonlinear stability of weak detonation waves for a combustion model

We show that the weak detonation waves for a combustion model of Rosales-Ma jda 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 particul ar, the propagation of the wave depends sensitively on the tail behaviour o f the flow in front of it. Unlike the strong detonation waves, a weak deton ation is supersonic and there is the separation of the gas waves from the r eacting front. As a consequence, the reacting front needs to be traced.