Optimal control of a phase field system modelling tumor growth with chemotaxis and singular potentials
arXiv:1907.03566 · doi:10.1007/s00245-019-09618-6
Abstract
A distributed optimal control problem for an extended model of phase field type for tumor growth is addressed. In this model, the chemotaxis effects are also taken into account. The control is realized by two control variables that design the dispensation of some drugs to the patient. The cost functional is of tracking type, whereas the potential setting has been kept quite general in order to allow regular and singular potentials to be considered. In this direction, some relaxation terms have been introduced in the system. We show the well-posedness of the state system, the Fréchet differentiability of the control-to-state operator in a suitable functional analytic framework, and, lastly, we characterize the first-order necessary conditions of optimality in terms of a variational inequality involving the adjoint variables.
References in corpus (10)
- A coupled surface-Cahn--Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes
- A multiphase Cahn-Hilliard-Darcy model for tumour growth with necrosis
- Optimal distributed control of a diffuse interface model of tumor growth
- Long-time Dynamics and Optimal Control of a Diffuse Interface Model for Tumor Growth
- Optimal Distributed Control of a Cahn-Hilliard-Darcy System with Mass Sources
- Optimal distributed control of an extended model of tumor growth with logarithmic potential
- Optimal control theory and advanced optimality conditions for a diffuse interface model of tumor growth
- Optimal medication for tumors modeled by a Cahn-Hilliard-Brinkman equation
- Optimality conditions for an extended tumor growth model with double obstacle potential via deep quench approach
- Optimal treatment for a phase field system of Cahn-Hilliard type modeling tumor growth by asymptotic scheme