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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.AP2024
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…