33 citations · 171 across the 49 of their papers we have counts for
6 papers · 2 filters
On a phase field model of Cahn-Hilliard type for tumour growth with mechanical effects
Harald Garcke, Kei Fong Lam, Andrea Signori
Mechanical effects have mostly been neglected so far in phase field tumour models that are based on a Cahn-Hilliard approach. In this paper we study a macroscopic mechanical model…
Non-linear Stability of Double Bubbles under Surface Diffusion
Harald Garcke, Michael Gößwein
We consider the evolution of triple junction clusters driven by the surface diffusion flow. On the triple line we use the boundary conditions derived by Garcke and Novick-Cohen as…
On the Surface Diffusion Flow with Triple Junctions in Higher Space Dimensions
Harald Garcke, Michael Gößwein
We show short time existence for the evolution of triple junction clusters driven by the surface diffusion flow. On the triple line we use the boundary conditions derived by Garcke…
Stability analysis for stationary solutions of the Mullins-Sekerka flow with boundary contact
Harald Garcke, Maximilian Rauchecker
We first give a complete linearized stability analysis around stationary solutions of the Mullins-Sekerka flow with contact angle in two space dimensions. The stationary…
On a degenerate parabolic system describing the mean curvature flow of rotationally symmetric closed surfaces
Harald Garcke, Bogdan-Vasile Matioc
We show that the mean curvature flow for a closed and rotationally symmetric surface can be formulated as an evolution problem consisting of an evolution equation for the square of…
Long Time Existence of Solutions to an Elastic Flow of Networks
Harald Garcke, Julia Menzel, Alessandra Pluda
The --gradient flow of the elastic energy of networks leads to a Willmore type evolution law with nontrivial nonlinear boundary conditions. We show local in time existence and…