24 citations · 72 across the 28 of their papers we have counts for
3 papers · 2 filters
Dynamics of curved travelling fronts for the discrete Allen-Cahn equation on a two-dimensional lattice
Mia Jukić, Hermen Jan Hupkes
In this paper we consider the discrete Allen-Cahn equation posed on a two-dimensional rectangular lattice. We analyze the large-time behaviour of solutions that start as bounded pe…
Counting and ordering periodic stationary solutions of lattice Nagumo equations
Hermen Jan Hupkes, Leonardo Morelli, Petr Stehlík +1
We study the rich structure of periodic stationary solutions of Nagumo reaction diffusion equation on lattices. By exploring the relationship with Nagumo equations on cyclic graphs…
Multichromatic travelling waves for lattice Nagumo equations
Hermen Jan Hupkes, Leonardo Morelli, Petr Stehlík +1
We discuss multichromatic front solutions to the bistable Nagumo lattice differential equation. Such fronts connect the stable spatially homogeneous equilibria with spatially heter…