Nonlinear Stability of Strong Detonation Waves for a Dissipative Model

We study the asymptotic behavior of solutions to a combustion model which contains the effect of convection, viscosity, chemical reaction, and diffusion. It is proved that if a perturbation of a travelling strong detonation wave is small, then the solution to this system converges to a strong detonation wave, which is the original one with a shift, ast→∞. The rate of convergence is also estimated