## Stability of strong detonation waves and rates of convergence

### Summary

Summary: In this article, we prove stability of strong detonation waves and find their rate of convergence for a combustion model. Our results read as follows: I) There exists a global solution that converges exponentially in time to a strong detonation wave, provided that the initial data is a small perturbation of a strong detonation wave that decays exponentially in |x|. II) When the initial perturbation decays algebraically in |x|, the solution converges algebraically in time. That is, the perturbation decays in t as `fast' as the initial perturbation decays in |x|.

### Mathematics Subject Classification

35L65, 35B40, 35B50, 76L05, 76J20

### Keywords/Phrases

strong detonation, shock wave, traveling wave, asymptotic behavior, weighted energy estimate