Multiple Traveling Waves for Dry Forward Combustion Through a Porous Medium

This paper involves the study of the existence and multiplicity of forward combustion fronts through a porous medium. The fronts are represented by traveling wave solutions of a system of three reaction-diffusion-convection equations, where the unknowns are the gas saturation, temperature, and volume fraction of the burned gas. In one regime, each pair of left and right states that can be connected by a traveling wave is connected by exactly two traveling waves with distinct speeds. For more general regimes and certain pairs of left and right states, there are two distinct speed intervals, such that each endpoint of each interval denotes a speed for which a traveling wave connecting the states exists. The lengths of these intervals are not known; however, numerical simulations indicate that these intervals might be a single point. The results are proved using mainly the geometric singular perturbation theory and invariant regions.