9 citations · 19 across the 15 of their papers we have counts for
15 papers
A dispersive extension result for a class of nonlocal nonlinearities
Bastian Hilder, Christian Kuehn
We prove that a class of nonlocal nonlinearities on periodic Sobolev spaces can be expressed as a trace of the unique mild solution to a local dispersive problem consisting of a sy…
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…
Non-equilibrium functional inequalities for finite Markov chains
Bastian Hilder, Patrick van Meurs, Upanshu Sharma
Functional inequalities such as the Poincaré and log-Sobolev inequalities quantify convergence to equilibrium in continuous-time Markov chains by linking generator properties to va…
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 t…
Thermocapillary Thin Films: Periodic Steady States and Film Rupture
Gabriele Brüll, Bastian Hilder, Jonas Jansen
We study stationary, periodic solutions to the thermocapillary thin-film model \begin{equation*} \partial_t h + \partial_x \Bigl(h^3(\partial_x^3 h - g\partial_x h) + M\frac{h^2}{(…
Nonlinear stability of periodic roll solutions in the real Ginzburg-Landau equation against -perturbations
Bastian Hilder, Björn de Rijk, Guido Schneider
The real Ginzburg-Landau equation arises as a universal amplitude equation for the description of pattern-forming systems exhibiting a Turing bifurcation. It possesses spatially pe…
Quantitative coarse-graining of Markov chains
Bastian Hilder, Upanshu Sharma
Coarse-graining techniques play a central role in reducing the complexity of stochastic models, and are typically characterised by a mapping which projects the full state of the sy…
Modulating traveling fronts in a dispersive Swift-Hohenberg equation coupled to an additional conservation law
Bastian Hilder
We consider a one-dimensional Swift-Hohenberg equation coupled to a conservation law, where both equations contain additional dispersive terms breaking the reflection symmetry $x \…
An inequality connecting entropy distance, Fisher Information and large deviations
Bastian Hilder, Mark A. Peletier, Upanshu Sharma +1
In this paper we introduce a new generalisation of the relative Fisher Information for Markov jump processes on a finite or countable state space, and prove an inequality which con…
Modulating traveling fronts for the Swift-Hohenberg equation in the case of an additional conservation law
Bastian Hilder
We consider the one-dimensional Swift-Hohenberg equation coupled to a conservation law. As a parameter increases the system undergoes a Turing bifurcation. We study the dynamics ne…
Analysis of the embedded cell method for the numerical homogenization of metal-ceramic composite materials
Wolf-Patrick Düll, Bastian Hilder, Guido Schneider
In this paper, we analyze the embedding cell method, an algorithm which has been developed for the numerical homogenization of metal-ceramic composite materials. We show the conver…