Recent results on stability of planar detonations

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.