A Geometric Singular Perturbation Analysis of Detonation and Deflagration Waves

The existence of steady plane wave solutions of the Navier-Stokes equations for a reacting gas is analyzed. Under the assumption of an ignition temperature the existence of detonation and deflagration waves close to the corresponding waves of the ZND-model is proved in the limit of small viscosity, heat conductivity, and diffusion. The method is constructive, since the classical solutions of the ZND-model serve as singular solutions in the context of geometric singular perturbation theory. The singular solutions consist of orbits on which the dynamics are slow-driven by chemical reaction and of orbits on which the dynamics are fast-driven by gasdynamic shocks. The approach is geometric and leads to a clear, complete picture of the existence, structure, and asymptotic behavior of detonation and deflagration waves.