A GEOMETRIC SINGULAR PERTURBATION ANALYSIS OF DETONATION AND DEFLAGRATION WAVES

The existence of steady plane wave solutions of the Navier-Stokes equa tions for a reacting gas is analyzed. Under the assumption of an ignit ion temperature the existence of detonation and deflagration waves clo se to the corresponding waves of the ZND-model is proved in the limit of small viscosity, heat conductivity, and diffusion. The method is co nstructive, since the classical solutions of the ZND-model serve as si ngular solutions in the context of geometric singular perturbation the ory. The singular solutions consist of orbits on which the dynamics ar e slow-driven by chemical reaction and of orbits on which the dynamics are fast-driven by gasdynamic shocks. The approach is geometric and l eads to a clear, complete picture of the existence, structure, and asy mptotic behavior of detonation and deflagration waves.