Journal of Statistical Physics, Vol. 90, Nos. 5/6, 1998, p. 1401-1411.
We study the nucleation and growth of flame fronts in slow combustion. This is modeled by a set of reaction-diffusion equations for the temperature field, coupled to a background of reactants and augmented by a term describing random temperature fluctuations for ignition. We establish connections between this model and the classical theories of nucleation and growth of droplets from a metastable phase. Our results are in good agreement with theoretical predictions.