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

TL;DR

This paper proves the existence and uniqueness of traveling ignition fronts in a reaction-diffusion model for reactive jets, using dynamical systems methods.

Contribution

It establishes the existence and uniqueness of traveling front solutions in a free boundary reaction-diffusion model for autoignition in reactive jets.

Findings

Existence of a unique traveling front solution up to translation.

Application of dynamical systems techniques like the Stable Manifold Theorem.

Use of Melnikov integral in the analysis.

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.