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.
1
ENSMM, Besançon and Université de Bourgogne Franche-Comté, Besançon, France
Nathaël Alibaud; Gawtum Namah. On the propagation of a periodic flame front by an Arrhenius kinetic. Interfaces and free boundaries, Tome 19 (2017) no. 3, pp. 449-494. doi: 10.4171/ifb/389
@article{10_4171_ifb_389,
author = {Natha\"el Alibaud and Gawtum Namah},
title = {On the propagation of a periodic flame front by an {Arrhenius} kinetic},
journal = {Interfaces and free boundaries},
pages = {449--494},
year = {2017},
volume = {19},
number = {3},
doi = {10.4171/ifb/389},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/389/}
}
TY - JOUR
AU - Nathaël Alibaud
AU - Gawtum Namah
TI - On the propagation of a periodic flame front by an Arrhenius kinetic
JO - Interfaces and free boundaries
PY - 2017
SP - 449
EP - 494
VL - 19
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/389/
DO - 10.4171/ifb/389
ID - 10_4171_ifb_389
ER -
%0 Journal Article
%A Nathaël Alibaud
%A Gawtum Namah
%T On the propagation of a periodic flame front by an Arrhenius kinetic
%J Interfaces and free boundaries
%D 2017
%P 449-494
%V 19
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/389/
%R 10.4171/ifb/389
%F 10_4171_ifb_389
