21 citations · 33 across the 22 of their papers we have counts for
7 papers · 2 filters
Short Time Existence for the Curve Diffusion Flow with a Contact Angle
Helmut Abels, Julia Butz
We show short-time existence for curves driven by curve diffusion flow with a prescribed contact angle : The evolving curve has free boundary points, which are support…
On the Sharp Interface Limit of a Model for Phase Separation on Biological Membranes
Helmut Abels, Johannes Kampmann
We rigorously prove the convergence of weak solutions to a model for lipid raft formation in cell membranes which was recently proposed by Garcke et al. to weak (varifold) solution…
A Blow-up Criterion for the Curve Diffusion Flow with a Contact Angle
Helmut Abels, Julia Butz
We prove a blow-up criterion in terms of an -bound of the curvature for solutions to the curve diffusion flow if the maximal time of existence is finite. In our setting, we co…
On a Model for Phase Separation on Biological Membranes and its Relation to the Ohta-Kawasaki Equation
Helmut Abels, Johannes Kampmann
We provide a detailed mathematical analysis of a model for phase separation on biological membranes which was recently proposed by Garcke, Rätz, Röger and the second author. The mo…
Convergence of the Allen-Cahn Equation to the Mean Curvature Flow with -Contact Angle in 2D
Helmut Abels, Maximilian Moser
We consider the sharp interface limit of the Allen-Cahn equation with homogeneous Neumann boundary condition in a two-dimensional domain , in the situation where an interface ha…
Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different Densities and Nonlocal Free Energies
Helmut Abels, Yutaka Terasawa
We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids with different densities in a bounded domain in two a…