3 papers
math.DS2022
Propagation reversal for bistable differential equations on trees
Hermen Jan Hupkes, Mia Jukić, Petr Stehlík +1
We study traveling wave solutions to bistable differential equations on infinite -ary trees. These graphs generalize the notion of classical square infinite lattices and our res…
math.DS2021
Curvature-driven front propagation through planar lattices in oblique directions
Mia Jukić, Hermen Jan Hupkes
In this paper we investigate the long-term behaviour of solutions to the discrete Allen-Cahn equation posed on a two-dimensional lattice. We show that front-like initial conditions…
math.DS2019
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…