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Multiplicity and stability of travelling wave solutions in a free boundary combustion-radiation problem

Published online by Cambridge University Press:  14 April 2004

OLIVIER BACONNEAU ,
JAN BOUWE VAN DEN BERG ,
CLAUDE-MICHEL BRAUNER  and
JOSEPHUU HULSHOF
OLIVIER BACONNEAU
Affiliation:
Université Bordeaux I, Mathématiques Appliquées de Bordeaux, 33405 Talence Cedex, France
JAN BOUWE VAN DEN BERG
Affiliation:
Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands email: janbouwe@few.vu.nl
CLAUDE-MICHEL BRAUNER
Affiliation:
Université Bordeaux I, Mathématiques Appliquées de Bordeaux, 33405 Talence Cedex, France email: brauner@math.u-bordeaux.fr
JOSEPHUU HULSHOF
Affiliation:
Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands email: jhulshof@few.vu.nl
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Abstract

We study travelling wave solutions of a one-dimensional two-phase Free Boundary Problem, which models premixed flames propagating in a gaseous mixture with dust. The model combines diffusion of mass and temperature with reaction at the flame front, the reaction rate being temperature dependent. The radiative effects due to the presence of dust account for the divergence of the radiative flux entering the equation for temperature. This flux is modelled by the Eddington equation. In an appropriate limit the divergence of the flux takes the form of a nonlinear heat loss term. The resulting reduced model is able to capture a hysteresis effect that appears if the amount of fuel in front of the flame, or equivalently, the adiabatic temperature is taken as a control parameter.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 15 , Issue 1 , February 2004 , pp. 79 - 102
Copyright
© 2004 Cambridge University Press

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