Dynamical velocity selection: Marginal stability

Abstract

Dee et al. have advanced the idea that the natural velocity of fronts propagating into an unstable state is related to the stability of these fronts through ‘‘marginal stability.’’ It is shown that this is indeed the case if front solutions lose stability through one particular mechanism. Marginal stability is derived for front propagation in the Swift-Hohenberg equation, but does not hold in a certain range of parameters of an extension of the Fisher-Kolmogorov equation.