188 citations · 1.6k across the 107 of their papers we have counts for
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Well-posedness of a Cahn--Hilliard system modelling tumour growth with chemotaxis and active transport
Harald Garcke, Kei Fong Lam
We consider a diffuse interface model for tumour growth consisting of a Cahn--Hilliard equation with source terms coupled to a reaction-diffusion equation. The coupled system of pa…
A coupled surface-Cahn--Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes
Harald Garcke, Johannes Kampmann, Andreas Rätz +1
We propose and investigate a model for lipid raft formation and dynamics in biological membranes. The model describes the lipid composition of the membrane and an interaction with…
A Cahn--Hilliard--Darcy model for tumour growth with chemotaxis and active transport
Harald Garcke, Kei Fong Lam, Emanuel Sitka +1
Using basic thermodynamic principles we derive a Cahn--Hilliard--Darcy model for tumour growth including nutrient diffusion, chemotaxis, active transport, adhesion, apoptosis and p…
Segmentation of Three-dimensional Images with Parametric Active Surfaces and Topology Changes
Heike Benninghoff, Harald Garcke
In this paper, we introduce a novel parametric method for segmentation of three-dimensional images. We consider a piecewise constant version of the Mumford-Shah and the Chan-Vese f…
Standard Planar Double Bubbles are Stable under Surface Diffusion Flow
Helmut Abels, Nasrin Arab, Harald Garcke
Although standard planar double bubbles are stable in the sense that the second variation of the perimeter functional is non-negative for all area-preserving perturbations the ques…
Segmentation and Restoration of Images on Surfaces by Parametric Active Contours with Topology Changes
Heike Benninghoff, Harald Garcke
In this article, a new method for segmentation and restoration of images on two-dimensional surfaces is given. Active contour models for image segmentation are extended to images o…