Traveling Wave Solutions to Combustion Models and Their Singular Limits

We consider the deflagration wave problem for a compressible reacting gas, with species involved in a single step chemical reaction. In the limit of small Mach numbers, the one-dimensional traveling wave problem reduces to a system of reaction-diffusion equations. Existence is proved by first considering the problem in a bounded domain, and taking an infinite domain limit. In the singular limit of high activation energy within the Arrhenius exponential reaction term, we prove strong convergence to a limiting free boundary problem; the latter is characterized by a jump of the derivatives, which we determine.