Front propagation: precursors, cutoffs, and structural stability

D. Kessler, Z Ner, LM Sander

Research output: Contribution to journalArticlepeer-review


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 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.
Original languageAmerican English
Pages (from-to)107-114
JournalPhysical Review E (Statistical, Nonlinear, and Soft Matter Physics)
Issue number1
StatePublished - 1998


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