Speed of fronts of generalized reaction-diffusion equations

Recent work on generalized diffusion equations has given analytical and numerical evidence that, as in the standard reaction-diffusion equation, most initial conditions evolve into a traveling wave which corresponds 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 marginal stability value) and provide upper and lower bounds on the speed. This enables us to characterize the functions for which linear marginal stability holds and also to provide a tool to calculate the speed when the marginal value does not predict its correct value.