  We introduce a phase-field model to describe the dynamics of a
self-sustaining propagating combustion front within a medium of randomly
distributed reactants. Numerical simulations of this model show that a flame
front exists for reactant concentration $c > c^* > 0$, while its vanishing at
$c^*$ is consistent with mean-field percolation theory. For $c > c^*$, we find
that the interface associated with the diffuse combustion zone exhibits kinetic
roughening characteristic of the Kardar-Parisi-Zhang equation.
