On large scale forest fires propagation models

The question of the modeling of forest fires at large scales is addressed. Empirical models are compared and it is shown that Rothermel's model describing the rate of spread of a straight front is included in the envelope model which in turn is included in a Hamilton–Jacobi equation description. This result shows that the preceding models could be included in reaction diffusion systems. Then an anisotropic propagation model with a nonlocal radiative term, obtained by asymptotic expansion of a combustion modeling, is proposed. This modeling takes into account the effects of wind and slope and it is shown that this type of modeling is the simplest generalization of the empirical ones.