Abstract. We focus on a reaction–diffusion approach proposed recently for experiments on combustion processes, where the heat released by combustion follows first-order reaction kinetics. This case allows us to perform an exhaustive analytical study. Specifically, we obtain the exact expressions for the speed of the thermal pulses, their maximum temperature and the condition of self-sustenance. Finally, we propose two generalizations of the model, namely, the case of several reactants burning together, and that of time-delayed heat conduction. We find an excellent agreement between our analytical results and simulations.

PACS numbers: 05.40.−a, 89.20.−a

Print publication: Issue 26 (2 July 2004)
Received 28 January 2004, in final form 14 April 2004
Published 16 June 2004