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math.AP2025
Equivalence of weak solution concepts for mean curvature flow
Tim Laux, Anton Ullrich
We provide a connection between weak solution concepts of mean curvature flow. On the one side we have the viscosity solution which is based on the comparison principle. On the oth…
math.AP2025
Generic mean curvature flow with obstacles
Tim Laux, Keisuke Takasao
We study the obstacle problem associated to mean curvature flow. We add to the geometric vanishing-viscosity approximation of Evans and Spruck a singular perturbation that penalize…
math.AP2025
Change of bifurcation type in 2D free boundary model of a moving cell with nonlinear diffusion
Leonid Berlyand, Oleksii Krupchytskyi, Tim Laux
We introduce a 2D free boundary problem with nonlinear diffusion that models a living cell moving on a substrate. We prove that this nonlinearity results in a qualitative of soluti…