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math.AP2025
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…
math.AP2025
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…
math.AP2025
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…