Propagation of Flames in the Limit of Zero Ignition Temperature

Abstract

This paper is devoted to the study of planar deflagration flames. The combustion takes place in a gaseous mixture in which N chemical species B ₁,…,B _N are subject to a complex chemical network of R chemical reactions:

In the limit of zero ignition temperature, existence of traveling waves for any speed in a range [c ₀,+∞) is proved for exothermic networks. Non-existence is proved for c∈(0,c ^*). A new index argument is introduced which is of independent interest. In the case of Lewis number less than 1 and of non-competitive networks, the set of speeds is exactly the interval [c ₀,+∞) (c ₀ = c ^*).