On the propagation of a periodic flame front by an arrhenius kinetic

TL;DR

This paper studies how a flame front propagates through a periodically structured solid medium, considering Arrhenius kinetics and curvature effects, and explores the existence and homogenization of traveling wave solutions.

Contribution

It establishes the existence of traveling wave solutions for a free boundary system with Arrhenius kinetics and analyzes their homogenization as the period approaches zero.

Findings

Existence of traveling wave solutions for the system.

Homogenization results as the period tends to zero.

Curvature effects influence the limiting wave behavior.

Abstract

We consider the propagation of a flame front in a solid medium with a periodic structure. The model is governed by a free boundary system for the pair" temperature-front. "The front's normal velocity depends on the temperature via a (degenerate) Arrhenius kinetic. It also depends on the front's mean curvature. We show the existence of travelling wave solutions for the full system and consider their homogenization as the period tends to zero. We analyze the curvature effects on the homogenization and obtain a continuum of limiting waves parametrized by the limiting ratio "curvature coefficient/period." This analysis provides valuable information on the heterogeneous propagation as well.