Abstract :
The initiation problem for a combustion model is studied. Global existence of the solution to the problem is established and the asymptotic behavior of the solution is studied. Specifically, we prove that the solution converges to a self-sustaining detonation wave, i.e., the minimal travelling wave, or the CJ detonation wave, followed by a rarefaction wave provided that the initial pulse is large. If the data are small, the solution decays to zero like an N-wave.
