Traveling waves in combustion processes with complex chemical networks

The existence of traveling waves for laminar flames with complex chemistry is proved. The crucial assumptions are that all reactions have to be exothermic and that no cycles occur in the graph of the reaction network. The method is to solve the equations first in a bounded interval by a degree argument and then taking the infinite domain limit. 0. Introduction. In this paper we establish the existence of traveling waves for premixed laminar flames with complex chemical networks. We consider the case of vanishing Mach number i.e. the flame speed is much smaller than a typical gas . ve SOClty. The resulting equations were solved by H. Berestycki, B. Nicolaenko, B. Scheurer [1] for a single step irreversible reaction. Here we discuss a class of exothermic acyclic chemical networks. In [2 3] P. Fife and B. Nicolaenko used a somewhat weaker condition on the network than ours for a formal asymptotic analysis in the limit of high activation energy. For mathematical reasons we can only handle the case of exothermic, i.e. irreversible reactions. In the first section we introduce the notations and derive the traveling wave equations from the thermodynamic conservation laws. In §2 these equations are solved in a finite domain by a mapping degree argument and then shown to converge in the infinite domain limit. The third section treats some examples to which the existence theorem can be applied. 1. Notations and derivation of the traveling wave equations. Let t be the mass functions of n chemical species A, reacting in an infinite tube and depending on time t and one space variable (. A chemical network consisting of r reactions may be symbolically written as