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math.AP2023★ 2 cited
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}{(…
math.AP2023★ 1 cited
Non-Newtonian thin-film equations: global existence of solutions, gradient-flow structure and guaranteed lift-off
Peter Gladbach, Jonas Jansen, Christina Lienstromberg
We study the gradient-flow structure of a non-Newtonian thin film equation with power-law rheology. The equation is quasilinear, of fourth order and doubly-degenerate parabolic. By…