H.J.Hupkes, D.E. Pelinovsky, and B. Sandstede

Propagation failure in the discrete Nagumo equation

Proceedings of the AMS, 139, 35373551 (2011)

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 travelling fronts in the discrete Nagumo equation with such special nonlinear functions appear to be similar to those in the continuous Nagumo equation.

Keywords:
lattice differential equation, propagation failure, discrete kink, normally hyperbolic invariant manifold