Existence and uniqueness of traveling fronts for a free interface model of autoignition in reactive jets

Abstract

In this paper we consider a one-dimensional reaction-diffusion model with piecewise continuous reaction term that describes propagation of autoignition fronts in reactive co-flow jets in a certain parametric regime. The model is reduced to a free boundary problem with two interfaces. It is shown that this problem admits permanent traveling front solution which is unique up to translations. The result is obtained using dynamical system approach employing Stable Manifold Theorem and the Melnikov integral as the main tools.