Asymptotic analysis of a parabolic system arising in combustion theory (Q1028507)

The authors are concerned with a classical reaction-diffusion system which describes the flame propagation with Lewis number close to one, and the reaction rate is assumed to be of Arrhenius type. The authors first prove estimates on the solutions that are independent of the activation energy. Next, they investigate the high activation energy asymptotic behavior and derive the limiting free boundary problem. The limiting system obtained coincides with the one formally derived by physicists. The main results of this paper justifies the reduced model commonly used in applications.