Electron. J. Diff. Eqns., Vol. 1998(1998), No. 09, pp. 1-17.
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|.
Submitted October 14, 1997. Published March 18, 1998.
Math Subject Classification: 35L65, 35B40, 35B50, 76L05, 76J20.
Key Words: Strong detonation, shock wave, traveling wave, asymptotic behavior, weighted energy estimate.
Show me the PDF file (162 KB), TEX file, and other files for this article.