10 papers
Generic Mean Curvature Flow With Rough Weights
Fabius Krämer, Tim Laux, Keisuke Takasao
We prove the generic existence of mean curvature flows in spaces with rough weights. Our weak solutions are both unit-density Brakke flows and distributional solutions. Such a gene…
Strong Convergence of Continuous Median Filter Scheme
Fabius Krämer, Tim Laux
We introduce a continuous-time counterpart of the median filter that gradually denoises a given image. In the limit of vanishing stencil size, our results show that the evolution c…
Convergence of a vector-valued Allen-Cahn system to Brakke's multiphase mean curvature flow
Tim Laux, Keisuke Takasao
Since Ilmanen's pioneering work [J. Differential Geom. 38, 417-461, (1993)] it has been a major open problem to understand the sharp-interface limit of systems of coupled Allen-Cah…
The Verigin problem with phase transition as a Wasserstein flow
Anna Kubin, Tim Laux, Alice Marveggio
We study the modeling of a compressible two-phase flow in a porous medium. The governing free boundary problem is known as the Verigin problem with phase transition. We introduce a…
Obstacle Mean Curvature Flow: Efficient Approximation and Convergence Analysis
Fabius Krämer, Tim Laux
We introduce a simple and efficient numerical method to compute mean curvature flow with obstacles. The method augments the Merrimam-Bence-Osher scheme with a pointwise update that…
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…
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…
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…
An efficient volume-preserving MBO scheme for data clustering and classification
Fabius Krämer, Tim Laux
We propose and study a novel efficient algorithm for clustering and classification tasks based on the famous MBO scheme. On the one hand, inspired by Jacobs et al. [J. Comp. Phys.…
Median filter method for mean curvature flow using a random Jacobi algorithm
Anton Ullrich, Tim Laux
We present an efficient scheme for level set mean curvature flow using a domain discretization and median filters. For this scheme, we show convergence in -norm under mil…