On Spinning Propagation of Combustion Waves

We consider a system of reaction-diffusion equations describing the propagation of combustion waves along a thermally insulated cylindrical sample of solid fuel. Uniform propagation of a plane combustion wave is subjected to a linear stability analysis. It is shown that, if the activation energy is sufficiently high and the diameter of the sample sufficiently large, then the experimentally observed spinning propagation of combustion waves appears as a Hopf-type bifurcation of the solution corresponding to a plane wave. The possibility of similar phenomena in gas combustion is discussed.