Recent results on stability of planar detonations

TL;DR

This paper reviews recent analytical and numerical findings on the stability of planar detonation waves, emphasizing viscous and inviscid cases, and explores high-frequency stability in multi-dimensional settings using advanced mathematical techniques.

Contribution

It provides a comprehensive overview of recent advances in the stability analysis of planar detonations, including new results on inviscid high-frequency stability and the application of dynamical systems methods.

Findings

Viscous and inviscid stability results for 1D perturbations.

High-frequency stability analysis in multi-D detonations.

Application of Evans function and WKB techniques to detonation stability.

Abstract

We describe recent analytical and numerical results on stability and behavior of viscous and inviscid detonation waves obtained by dynamical systems/Evans function techniques like those used to study shock and reaction diffusion waves. In the first part, we give a broad description of viscous and inviscid results for 1D perturbations; in the second, we focus on inviscid high-frequency stability in multi-D and associated questions in turning point theory/WKB expansion.