D. Pelinovsky
Traveling monotonic fronts in the discrete Nagumo equation
Journal of Dynamics in Differential Equations 23, 167–183 (2011)
Abstract:
We give an alternative proof of the theorem, which states that no propagation
failure occurs for the discrete Nagumo equation with “translationally invariant” stationary
monotonic fronts. The theorem was recently proved with the use of the invariant manifolds
for lattice differential equations by Hupkes, Pelinovsky, and Sandstede. The alternative proof
relies on the analysis of the advance-delay operator associated with the translationally invariant
stationary front. This operator exhibits an infinite-dimensional kernel spanned by Fourier
harmonics of front’s translations, which are accounted when the stationary front is continued
into the traveling one.
Keywords:
lattice differential equations, differential advance-delay operators,
propagation failure, discrete kink, singular perturbation theory