The article presents the analysis of a simplified one-dimensional model of combustion that includes the effects of compressibility, diffusion, heat conduction, viscosity, and exothermic heat release. Using numerical simulations, it is shown that the model predicts both detonation-like and deflagration-like traveling waves. Importantly, it also predicts spontaneous transition from deflagration to detonation in the problem of hot-spot ignition from a closed end of a channel.