We consider a one-dimensional parabolic system which describes the propagation of a flame with Lewis number close to one. We first prove estimates on the solutions that are independent of the activation energy. Next, we investigate the high activation energy asymptotics and derive the limiting free boundary problem. Our results rigorously justify the models currently used by physicists.
"Asymptotic analysis of a parabolic system arising in combustion theory." Adv. Differential Equations 14 (1/2) 55 - 86, January/February 2009.