Electronic Journal of Differential Equations,
Vol. 1998(1998), No. 09, pp. 1-17.

Title: Stability of strong detonation waves and rates of convergence

Author: Tong Li (Univ. of Iowa, Iowa City, USA)

Abstract: 
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.