51 citations · 168 across the 26 of their papers we have counts for
14 papers · 1 filter
Chaotic motion and singularity structures of front solutions in multi-component FitzHugh-Nagumo-type systems
Martina Chirilus-Bruckner, Peter van Heijster, Jens D. M. Rademacher
We study the dynamics of front solutions in a certain class of multi-component reaction-diffusion systems, where one fast component governed by an Allen-Cahn equation is weakly cou…
Fractional Dissipative PDEs
Franz Achleitner, Goro Akagi, Christian Kuehn +4
In this chapter we provide an introduction to fractional dissipative partial differential equations (PDEs) with a focus on trying to understand their dynamics. The class of PDEs we…
Weak and strong interaction of excitation kinks in scalar parabolic equations
Antoine Pauthier, Jens D. M. Rademacher, Dennis Ulbrich
Motivated by studies of the Greenberg-Hastings cellular automata (GHCA) as a caricature of excitable systems, in this paper we study kink-antikink dynamics in the perhaps simplest…
Explicit superposed and forced plane wave generalized Beltrami flows
Artur Prugger, Jens D. M. Rademacher
We revisit and present new linear spaces of explicit solutions to incompressible Euler and Navier-Stokes equations on , as well as the rotating Boussinesq equations o…
The impact of advection on the stability of stripes on lattices near planar Turing instabilities
Jichen Yang, Jens D. M. Rademacher, Eric Siero
Striped patterns are known to bifurcate in reaction-diffusion systems with differential isotropic diffusions at a supercritical Turing instability. In this paper we study the impac…
The impact of advection on large-wavelength stability of stripes near planar Turing instabilities
Jichen Yang, Jens D. M. Rademacher, Eric Siero
It is well known that for reaction-diffusion systems with differential isotropic diffusions, a Turing instability yields striped solutions. In this paper we study the impact of wea…
Reaction-subdiffusion systems and memory: spectra, Turing instability and decay estimates
Jichen Yang, Jens D. M. Rademacher
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial…
Inhomogeneous domain walls in spintronic nanowires
Lars Siemer, Ivan Ovsyannikov, Jens D. M. Rademacher
In case of a spin-polarized current, the magnetization dynamics in nanowires are governed by the classical Landau-Lifschitz equation with Gilbert damping term, augmented by a typic…
Unfolding symmetric Bogdanov-Takens bifurcations for front dynamics in a reaction-diffusion system
Martina Chirilus-Bruckner, Peter van Heijster, Hideo Ikeda +1
This manuscript extends the analysis of a much studied singularly perturbed three-component reaction-diffusion system for front dynamics in the regime where the essential spectrum…
Spectra and stability of spatially periodic pulse patterns: Evans function factorization via Riccati transformation
Björn de Rijk, Arjen Doelman, Jens Rademacher
In the spectral stability analysis of localized patterns to singular perturbed evolution problems, one often encounters that the Evans function respects the scale separation. In su…
pde2path - version 2.0: faster FEM, multi-parameter continuation, nonlinear boundary conditions, and periodic domains - a short manual
Tomas Dohnal, Jens D. M. Rademacher, Hannes Uecker +1
pdepath 2.0 is an upgrade of the continuation/bifurcation package pde2path for elliptic systems of PDEs over bounded 2D domains, based on the Matlab pdetoolbox. The new features in…
Patterns formation in axially symmetric Landau-Lifshitz-Gilbert-Slonczewski equations
Christof Melcher, Jens D. M. Rademacher
The Landau-Lifshitz-Gilbert-Slonczewski equation describes magnetization dynamics in the presence of an applied field and a spin polarized current. In the case of axial symmetry an…
Global stability and local bifurcations in a two-fluid model for tokamak plasma
D. Zhelyazov, D. Han-Kwan, J. D. M. Rademacher
We study a two-fluid description of high and low temperature components of the electron velocity distribution of an idealized tokamak plasma. We refine previous results on the lami…
pde2path - A Matlab package for continuation and bifurcation in 2D elliptic systems
Hannes Uecker, Daniel Wetzel, Jens D. M. Rademacher
pde2path is a free and easy to use Matlab continuation/bifurcation package for elliptic systems of PDEs with arbitrary many components, on general two dimensional domains, and with…