Front propagation for reaction–diffusion equations arising in combustion theory

Abstract

In this paper we study the rigorous connections between reaction–diffusion equations of ZFK-type, which arise as simple models in combustion theory, and the propagating fronts, i.e., propagating flames, they generate for large times. Our main result is that the associated fronts propagate globally in time with normal velocity equal to the speed of the stable travelling wave associated with the reaction–diffusion equation. We point out that this result does not follow from any parts of the, by now, classical methods to study front propagation.