An Application of the Conley Index to Combustion

Abstract

This paper is concerned with the existence of laminar flames with complex chemistry. Mathematically, the problem reduces to proving the existence of traveling wave solutions of a reaction-diffusion system. The reaction-diffusion system takes the form

$$ U_t = DU_{xx} + F\left( U \right) $$

(1.1)

where U = (T,Y₁,...,Y_n−1) ∈ ℝⁿ and D is a positive, diagonal matrix. The components of U specify the dimensionless temperature and the concentration of the reactants. For a background of the physical motivation of these equations, see [2], [8].