Journal of Mathematical Chemistry Vol. 37, No. 2, February 2005 (© 2005) DOI: 10.1007/s10910-004-1447-7 The effect of ambient temperature on the propagation of nonadiabatic combustion waves V.V. Gubernov International Laser Center, M.V.Lomonosov Moscow State University, Moscow 119899, Russia and Department of Theoretical Physics, P.N. Lebedev Physical Institute of Russian Academy of Science, 53, Leninskii prospect, Moscow 119991, Russia H.S. Sidhu ∗ School of Physical, Environmental and Mathematical Sciences University of New South Wales at the Australian Defence Force Academy, Canberra, ACT 2600, Australia E-mail: h.sidhu@adfa.edu.au G.N. Mercer School of Physical, Environmental and Mathematical Sciences, University of New South Wales at the Australian Defence Force Academy, Canberra, ACT 2600, Australia Received 19 August 2004; revised 23 September 2004 In this paper, we undertake an analytical and numerical investigation of the linear stability and properties of travelling nonadiabatic combustion wave for the case of non- zero ambient temperature. Here we consider premixed fuel with one-step exothermic reaction described by Arrhenius law. The speed of the front is estimated analytically by employing the matched asymptotic expansion approach and numerically using the shooting and relaxation methods. It is shown that increasing the ambient temperature results in the growth of both the flame speed and the region of existence of the trav- elling wave solutions in the parameter space. The linear stability of the travelling wave solution is investigated analytically by using the matched asymptotic expansion method and numerically by employing the Evans function approach. We demonstrate that by increasing the ambient temperature the stability of the propagating wave can also be increased. KEY WORDS: combustion waves, heat loss, ambient temperature, Evans function AMS subject classification: 35K57, 80A25 1. Introduction The reaction-diffusion models describing the propagation of combustion waves have been the subject of ongoing study for sometime [1]. Much effort ∗ Corresponding author. 149 0259-9791/05/0200-0149/0 © 2005 Springer Science+Business Media, Inc.