Electron. J. Diff. Eqns., Vol. 1998(1998), No. 09, pp. 1-17.

Stability of strong detonation waves and rates of convergence

Tong Li

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.

Tong Li
Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
Telephone: 319-335-3342 Fax: 319-335-0627 e-mail: tli@math.uiowa.edu
Return to the EJDE home page