Detonation and Deflagration Waves with Multistep Reaction Schemes

The existence of traveling wave solutions of the Navier-Stokes equations for a chemically reacting gas is studied. As a specific example a three-component gas with a chain branching mechanism is considered. Under the assumption of an ignition temperature for the initiation reaction the existence of deflagration and detonation waves is proved in the limit of small viscosity, heat conductivity and diffusion. The constructive proof is based on methods from geometric singular perturbation theory. Qualitative differences to the already known case of a simple one-step reaction are discussed. A general method to prove the existence of combustion waves for a multi-component gas is presented.