Stability of planar wave solutions to combustion model

A system of reaction diffusion equations which arise as a model for a one-step combustion process is considered. The primary concern is with the stability of planar wave solutions to this model. This problem has been studied extensively from the point of view of matched asymptotics in the limit of infinite activation energy. The asymptotic analysis has demonstrated that for a large range of parameters, the planar wave solution is unstable. As a particular parameter is varied, the planar wave solution may undergo either a Hopf or steady state bifurcation. This paper gives a rigorous mathematical justification of some of the asymptotic results.