188 citations · 1.6k across the 107 of their papers we have counts for
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Optimal Control of time-discrete two-phase flow driven by a diffuse-interface model
Harald Garcke, Michael Hinze, Christian Kahle
We propose a general control framework for two-phase flows with variable densities in the diffuse interface formulation, where the distribution of the fluid components is described…
Finite Element Approximation for the Dynamics of Fluidic Two-Phase Biomembranes
John W. Barrett, Harald Garcke, Robert Nürnberg
Biomembranes and vesicles consisting of multiple phases can attain a multitude of shapes, undergoing complex shape transitions. We study a Cahn--Hilliard model on an evolving hyper…
On a Cahn--Hilliard--Darcy system for tumour growth with solution dependent source terms
Harald Garcke, Kei Fong Lam
We study the existence of weak solutions to a mixture model for tumour growth that consists of a Cahn--Hilliard--Darcy system coupled with an elliptic reaction-diffusion equation.…
Two-phase flow with surfactants: Diffuse interface models and their analysis
Helmut Abels, Harald Garcke, Kei Fong Lam +1
New diffuse interface and sharp interface models for soluble and insoluble surfactants fulfilling energy inequalities are introduced. We discuss their relation with the help of asy…
Global weak solutions and asymptotic limits of a Cahn--Hilliard--Darcy system modelling tumour growth
Harald Garcke, Kei Fong Lam
We study the existence of weak solutions to a Cahn--Hilliard--Darcy system coupled with a convection-reaction-diffusion equation through the fluxes, through the source terms and in…
Optimal control of treatment time in a diffuse interface model of tumor growth
Harald Garcke, Kei-Fong Lam, Elisabetta Rocca
We consider an optimal control problem for a diffuse interface model of tumor growth. The state equations couples a Cahn-Hilliard equation and a reaction-diffusion equation, which…