  We consider the propagation of a flame front in a solid medium with a
periodic structure. The model is governed by a free boundary system for the
pair" temperature-front. "The front's normal velocity depends on the
temperature via a (degenerate) Arrhenius kinetic. It also depends on the
front's mean curvature. We show the existence of travelling wave solutions for
the full system and consider their homogenization as the period tends to zero.
We analyze the curvature effects on the homogenization and obtain a continuum
of limiting waves parametrized by the limiting ratio "curvature
coefficient/period." This analysis provides valuable information on the
heterogeneous propagation as well.
