Unbounded Asymmetric Stationary Solutions of Lattice Nagumo Equations

Abstract

In this paper we provide a complete characterization of a class of unbounded asymmetric stationary solutions of the lattice Nagumo equations. We show that for any bistable cubic nonlinearity and arbitrary diffusion rate there exists a two-parametric set of equivalence classes of generally asymmetric stationary solutions which diverge to infinity. Our main tool is an iterative mirroring technique which could be applicable to other problems related to lattice equations. Finally, we generalize the result for a broad class of reaction functions.