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

Published online by Cambridge University Press:  14 November 2011

Joel D. Avrin
Joel D. Avrin
Affiliation:
Department of Mathematics, University of North Carolina at Charlotte, Charlotte, North Carolina 28223, U.S.A
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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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 117 , Issue 1-2 , 1991 , pp. 103 - 108
Copyright
Copyright © Royal Society of Edinburgh 1991

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