Traveling Monotonic Fronts in the Discrete Nagumo Equation |
| |
Authors: | Dmitry Pelinovsky |
| |
Institution: | (1) London School of Economics, London, UK |
| |
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: | |
本文献已被 SpringerLink 等数据库收录! |
|