Flame propagation in models of complex chemistry

We consider models of laminar flames with Arrhenius kinetics in long thin tubes. In previous studies of a model of a one-step reaction of the form A --> B, we identified certain conditions imposed on the initial temperature that guarantee a rough sense of flame propagation resulting in complete asymptotic burning of the fuel. We now extend these studies to a model of a two-step reaction of the form A --> B --> C, and to some models of one-step reactions with multiple species. We again identify sufficient conditions on the initial temperature that guarantee a rough sense of flame propagation and complete asymptotic burning. For these results to hold we need to add some restrictions on other parameters for technical reasons, but we show that our results nonetheless apply to a wide range of cases.