33 citations · 84 across the 5 of their papers we have counts for
6 papers
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…
Weak and stationary solutions to a Cahn-Hilliard-Brinkman model with singular potentials and source terms
Matthias Ebenbeck, Kei Fong Lam
We study a phase field model proposed recently in the context of tumour growth. The model couples a Cahn-Hilliard-Brinkman (CHB) system with a elliptic reaction-diffusion equation…
Optimal control theory and advanced optimality conditions for a diffuse interface model of tumor growth
Matthias Ebenbeck, Patrik Knopf
In this paper, we study a distributed optimal control problem for a diffuse interface model for tumor growth. The model consists of a Cahn-Hilliard type equation for the phase fiel…
On a Cahn-Hilliard-Brinkman model for tumour growth and its singular limits
Matthias Ebenbeck, Harald Garcke
In this work, we study a model consisting of a Cahn-Hilliard-type equation for the concentration of tumour cells coupled to a reaction-diffusion type equation for the nutrient dens…
Optimal medication for tumors modeled by a Cahn-Hilliard-Brinkman equation
Matthias Ebenbeck, Patrik Knopf
In this paper, we study a distributed optimal control problem for a diffuse interface model for tumor growth. The model consists of a Cahn-Hilliard type equation for the phase fiel…
Analysis of a Cahn-Hilliard-Brinkman model for tumour growth with chemotaxis
Matthias Ebenbeck, Harald Garcke
Phase field models recently gained a lot of interest in the context of tumour growth models. Typically Darcy-type flow models are coupled to Cahn-Hilliard equations. However, often…