# Optimal control theory and advanced optimality conditions for a diffuse interface model of tumor growth

@article{Ebenbeck2019OptimalCT, title={Optimal control theory and advanced optimality conditions for a diffuse interface model of tumor growth}, author={Matthias Ebenbeck and P. Knopf}, journal={arXiv: Optimization and Control}, year={2019} }

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 field variable coupled to a reaction diffusion equation for the nutrient and a Brinkman type equation for the velocity. The system is equipped with homogeneous Neumann boundary conditions for the tumor variable, the chemical potential and the nutrient as well as a "no-friction" boundary condition for the velocity. The… Expand

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