188 citations · 1.6k across the 107 of their papers we have counts for
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Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds
Harald Garcke, Robert Nürnberg
We present variational approximations of boundary value problems for curvature flow (curve shortening flow) and elastic flow (curve straightening flow) in two-dimensional Riemannia…
Sparse optimal control of a phase field tumour model with mechanical effects
Harald Garcke, Kei Fong Lam, Andrea Signori
In this paper, we study an optimal control problem for a macroscopic mechanical tumour model based on the phase field approach. The model couples a Cahn--Hilliard type equation to…
Shape and Topology Optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach
Harald Garcke, Paul Hüttl, Patrik Knopf
A cost functional involving the eigenvalues of an elastic structure, that is described by a multi-phase-field equation, is optimized. This allows us to handle topology changes and…
Long-time Dynamics for a Cahn-Hilliard Tumor Growth Model with Chemotaxis
Harald Garcke, Sema Yayla
Mathematical models that describe the tumor growth process have been formulated by several authors in order to understand how cancer develops and to develop new treatment approache…
Structure preserving discretisations of gradient flows for axisymmetric two-phase biomembranes
Harald Garcke, Robert Nürnberg
The form and evolution of multi-phase biomembranes is of fundamental importance in order to understand living systems. In order to describe these membranes, we consider a mathemati…
Cahn-Hilliard-Brinkman systems for tumour growth
Matthias Ebenbeck, Harald Garcke, Robert Nürnberg
A phase field model for tumour growth is introduced that is based on a Brinkman law for convective velocity fields. The model couples a convective Cahn-Hilliard equation for the ev…