24 citations · 72 across the 28 of their papers we have counts for
5 papers · 1 filter
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…
Micropteron traveling waves in diatomic Fermi-Pasta-Ulam-Tsingou lattices under the equal mass limit
Timothy E. Faver, Hermen Jan Hupkes
The diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) lattice is an infinite chain of alternating particles connected by identical nonlinear springs. We prove the existence of micropteron t…
Travelling Waves for Reaction-Diffusion Equations Forced by Translation Invariant Noise
Christian Hamster, Hermen Jan Hupkes
Inspired by applications, we consider reaction-diffusion equations on that are stochastically forced by a small multiplicative noise term that is white in time, colour…
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…