- journal article metadata
European Mathematical Society Publishing House
2017-10-13 23:40:01
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
19
2017
3
On the propagation of a periodic flame front by an Arrhenius kinetic
Nathaël
Alibaud
ENSMM, Besançon and Université de Bourgogne Franche-Comté, Besançon, France
Gawtum
Namah
ENSMM, Besançon and Université de Bourgogne Franche-Comté, Besançon, France
Free boundary problems, front propagation, combustion, Arrhenius law, travelling wave solutions, periodic solutions, homogenization, curvature effects, asymptotic analysis
We consider the propagation of a flame front in a solid periodic medium. The model is governed by a free boundary system in which the front’s velocity depends on the temperature via an Arrhenius kinetic. We show the existence of travelling wave solutions and consider their homogenization as the period tends to zero. The main difficulty lies in the degeneracy of the Arrhenius function which requires an a priori lower bound of the propagation’s speed. We next analyze the curvature effects on the homogenization and obtain a continuum of limiting waves parametrized by the ratio “curvature coefficient/period.” Remarkable features are the monotonicity of the speed with respect to the “curvature regime,” together with the explicit computations of the minimal and maximal speeds. We finally identify the asymptotic expansion of the heterogeneous front’s profile with respect to the period.
Partial differential equations
Classical thermodynamics, heat transfer
449
494
10.4171/IFB/389
http://www.ems-ph.org/doi/10.4171/IFB/389