7 papers · 1 filter
Global bifurcation of doubly periodic gravity-capillary waves on Beltrami flows
Bastian Hilder, Giang To, Erik Wahlén
We prove the existence of a global family of steady, doubly periodic gravity-capillary waves on Beltrami flows. This is the first rigorous existence result for genuinely three-dime…
Slow-moving pattern interfaces in general directions for a two-dimensional Swift-Hohenberg-type equation
Bastian Hilder, Jonas Jansen
We rigorously prove the bifurcation of slow-moving pattern interfaces with general direction in a two-dimensional Swift-Hohenberg-type model close to a Turing instability for a lar…
Pattern formation and nonlinear waves close to a 1:1 resonant Turing and Turing--Hopf instability
Bastian Hilder, Christian Kuehn
In this paper, we analyse the dynamics of a pattern-forming system close to simultaneous Turing and Turing--Hopf instabilities, which have a 1:1 spatial resonance, that is, they ha…
Pattern formation and film rupture in a two-dimensional thermocapillary thin-film model of the Bénard-Marangoni problem
Stefano Böhmer, Bastian Hilder, Jonas Jansen
We study two-dimensional, stationary square and hexagonal patterns in the thermocapillary deformational thin-film model for the fluid height \begin{equation*} \partial_t h+\nabl…
Linear convective stability of a front superposition with unstable connecting state
Louis Garénaux, Bastian Hilder
We study convective stability of a two-front superposition in a reaction-diffusion system. Due to the instability of the connecting equilibrium, long-range semi-strong interaction…
Fast-moving pattern interfaces close to a Turing instability in an asymptotic model for the three-dimensional Bénard-Marangoni problem
Bastian Hilder, Jonas Jansen
We study the bifurcation of planar patterns and fast-moving pattern interfaces in an asymptotic long-wave model for the three-dimensional Bénard-Marangoni problem, which is close…