Front Propagation: Precursors, Cutoffs and Structural Stability

We discuss the problem of fronts propagating into metastable and unstable states. We examine the time development of the leading edge, discovering a precursor which in the metastable case propagates out ahead of the front at a velocity more than double that of the front and establishes the characteristic exponential behavior of the steady-state leading edge. We also study the dependence of the velocity on the imposition of a cutoff in the reaction term. These studies shed new light on the problem of velocity selection in the case of propagation into an unstable state. We also examine how discreteness in a particle simulation acts as an effective cutoff in this case.