Propagation failure in the discrete Nagumo equation

Abstract

We address the classical problem of propagation failure for monotonic fronts of the discrete Nagumo equation. For a special class of nonlinearities that support unpinned "translationally invariant" stationary monotonic fronts, we prove that propagation failure cannot occur. Properties of traveling fronts in the discrete Nagumo equation with such special nonlinear functions appear to be similar to those in the continuous Nagumo equation. © 2011 American Mathematical Society.