Universal algebraic relaxation of fronts propagating into an unstable state and implications for moving boundary approximations

We analyze the relaxation of fronts propagating into unstable states. While "pushed" fronts relax exponentially like fronts propagating into a metastable state, "pulled" or "linear marginal stability" fronts relax algebraically. As a result, for thin fronts of this type. the standard moving boundary approximation fails. The leading relaxation terms for velocity and shape are of order 1/t and 1(/t3/2). These universal terms are calculated exactly with a new systematic analysis that unifies various heuristic approaches to front propagation.