| Abstract: | We derive and study asymptotic equations describing the behavior of low-frequency disturbances in a chemically reacting gas, whose amplitude is inversely proportional to the large activation energy of the reaction. We make an assumption of small heat release, so that fuel depletion is included in the model at leading order. For homogeneous combustion, introducing this assumption removes the thermal-runaway singularity which always forms in models previously used. We demonstrate that for spatially varying solutions, wave-propagation effects permit a singularity still to form, if the initial data has a step discontinuity with amplitude larger than a critical value. We suggest that appearance of this singularity in the model always signifies the birth of a detonation wave, and we describe the evolution of the wave beyond the singularity time. |
