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On the existence of premixed laminar flames

Published online by Cambridge University Press:  17 April 2009

Abdolrahman Razani
Abdolrahman Razani
Affiliation:
Institute for Studies in Theoretical, Physics and Mathematics (IPM), P.O. Box 19395–5746, Tehran, Iran, and Department of Mathematics, Faculty of Science, Imam Khomeini International University, P.O. Box 34194–288, Qazvin, Iran, e-mail: [email protected]
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In this article, the existence of travelling wave solutions for premixed laminar flames in a model of slow, “constant density” combustion is studied. The model is governed by a simple system of an exothermic chemical reaction in a gas, via the reaction rate function, which is very natural, as we do not impose the assumption of its continuity. The existence of travelling waves is demonstrated and they are shown to be specific heteroclinic orbits of a three dimensional system of ordinary differential equations, connecting the unburned state points to a burned state point. The existence of these solutions is based on some general topological arguments in ordinary differential equations.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 3 , June 2004 , pp. 415 - 427
Copyright
Copyright © Australian Mathematical Society 2004

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