SPEED OF FRONTS OF GENERALIZED REACTION-DIFFUSION EQUATIONS

Recent work on generalized diffusion equations has given analytical an d numerical evidence that, as in the standard reaction-diffusion equat ion, most initial conditions evolve into a traveling wave which corres ponds to a minimum speed front joining a stable to an unstable state. We show that this minimal speed derives from a variational principle; from this we recover linear constraints on the speed (the linear margi nal stability value) and provide upper and lower bounds on the speed. This enables us to characterize the functions for which linear margina l stability holds and also to provide a tool to calculate the speed wh en the marginal value does not predict its correct value.