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Behaviour at ±∞ for a model of laminar flames with applications to questions of flame propagation versus extinction

Synopsis We consider the behaviour at x = ±∞ of solutions to reaction-diffusion equations modelling laminar flames in a premixed reactive gas. We show that if the initial data have limits at ±∞, then the solutions satisfy ODEs at ±∞ for all positive time. We then analyse the qualitative behaviour of solutions to the ODEs. Our applications include extensions of previous results on questions of flame propagation versus extinction, and a new decay result: if the initial temperature is above ignition temperature at one end of the domani and if the initial concentration vanishes at the other, then we show that the concentration decays^to zero uniformly as the time variable goes to infinity.