Front propagation for reaction–diffusion equations arising in combustion theory

Article type: Research Article

Authors: Barles, G. | Georgelin, C. | Souganidis, P.E.

Affiliations: Faculté des Sciences et Techniques, Université de Tours, Parc de Grandmont, 37200 Tours, France | Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA

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.

DOI: 10.3233/ASY-1997-14304

Journal: Asymptotic Analysis, vol. 14, no. 3, pp. 277-292, 1997