Stability analysis for combustion fronts traveling in hydraulically resistant porous media

TL;DR

This paper investigates the spectral stability of combustion fronts in highly hydraulically resistant porous media, combining energy estimates and numerical Evans function computations to identify parameter regimes of stability.

Contribution

It introduces a novel analysis of stability for combustion fronts in resistant porous media, utilizing recent advances in partially parabolic systems theory.

Findings

Existence of parameter regimes with no unstable eigenvalues

Convective stability of fronts in the absence of unstable eigenvalues

Application of energy estimates and Evans function computations

Abstract

We study front solutions of a system that models combustion in highly hydraulically resistant porous media. The spectral stability of the fronts is tackled by a combination of energy estimates and numerical Evans function computations. Our results suggest that there is a parameter regime for which there are no unstable eigenvalues. We use recent works about partially parabolic systems to prove that in the absence of unstable eigenvalues the fronts are convectively stable.