In this short note we study the model of subsonic detonation introduced by Sivashinsky. The model is described by the system of reaction-diffusion equations involving temperature, pressure and concentration of deficient reactant. It is shown that initial data with small support lead to quenching (decay of solution). In contrast, initial data with support large enough lead to propagation with finite velocity.
"Quenching and propagation of combustion fronts in porous media." Commun. Math. Sci. 4 (2) 471 - 479, June 2006.