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This paper treats a distributed optimal control problem for a tumor growth model of viscous Cahn--Hilliard type. The evolution of the tumor fraction is governed by a thermodynamic force induced by a double-well potential of logarithmic…

Optimization and Control · Mathematics 2023-06-14 Jürgen Sprekels , Fredi Tröltzsch

In this paper, we study an optimal control problem for a nonlinear system of reaction-diffusion equations that constitutes a simplified and relaxed version of a thermodynamically consistent phase field model for tumor growth originally…

Optimization and Control · Mathematics 2020-08-25 Jürgen Sprekels , Fredi Tröltzsch

In this work, we investigate a distributed optimal control problem for an extended phase field system of Cahn--Hilliard type which physical context is that of tumor growth dynamics. In a previous contribution, the author has already studied…

Analysis of PDEs · Mathematics 2019-08-30 Andrea Signori

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…

Optimization and Control · Mathematics 2021-10-12 Matthias Ebenbeck , Patrik Knopf

A distributed optimal control problem for a phase field system which physical context is that of tumor growth is discussed. The system we are going to take into account consists of a Cahn-Hilliard equation for the phase variable (relative…

Analysis of PDEs · Mathematics 2021-01-20 Andrea Signori

We study a Cahn-Hilliard-Darcy system with mass sources, which can be considered as a basic, though simplified, diffuse interface model for the evolution of tumor growth. This system is equipped with an impermeability condition for the…

Optimization and Control · Mathematics 2024-08-20 Marco Abatangelo , Cecilia Cavaterra , Maurizio Grasselli , Hao Wu

In this paper, we study an optimal control problem for a macroscopic mechanical tumour model based on the phase field approach. The model couples a Cahn--Hilliard type equation to a system of linear elasticity and a reaction-diffusion…

Optimization and Control · Mathematics 2021-04-21 Harald Garcke , Kei Fong Lam , Andrea Signori

This paper concerns a distributed optimal control problem for a tumor growth model of Cahn-Hilliard type including chemotaxis with possibly singular potentials, where the control and state variables are nonlinearly coupled. First, we…

Optimization and Control · Mathematics 2023-06-06 Pierluigi Colli , Andrea Signori , Jürgen Sprekels

This paper investigates an optimal control problem associated with a two-dimensional multi-species Cahn-Hilliard-Keller-Segel tumor growth model, which incorporates complex biological processes such as species diffusion, chemotaxis,…

Analysis of PDEs · Mathematics 2024-07-26 Pierluigi Colli , Gianni Gilardi , Andrea Signori , Jürgen Sprekels

In this paper, we study an optimal control problem for a two-dimensional Cahn-Hilliard-Darcy system with mass sources that arises in the modeling of tumor growth. The aim is to monitor the tumor fraction in a finite time interval in such a…

Analysis of PDEs · Mathematics 2023-07-28 Juergen Sprekels , Hao Wu

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…

Analysis of PDEs · Mathematics 2021-03-23 Pierluigi Colli , Andrea Signori , Jürgen Sprekels

In this paper, the authors study the distributed optimal control of a system of three evolutionary equations involving fractional powers of three selfadjoint, monotone, unbounded linear operators having compact resolvents. The system is a…

Optimization and Control · Mathematics 2019-07-25 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

In this paper, we address an optimal distributed control problem for a non-local model of phase-field type, describing the evolution of tumour cells in presence of a nutrient. The model couples a non-local and viscous Cahn-Hilliard equation…

Analysis of PDEs · Mathematics 2023-10-25 Matteo Fornoni

In this paper, we study the optimal control of a phase field model for a tumor growth model of Cahn--Hilliard type in which the often assumed parabolic relaxation of the chemical potential is replaced by a hyperbolic one. Both the cases…

Optimization and Control · Mathematics 2026-03-17 Pierluigi Colli , Elisabetta Rocca , Jürgen Sprekels

This paper is intended to tackle the control problem associated with an extended phase field system of Cahn-Hilliard type that is related to a tumor growth model. This system has been investigated in previous contributions from the…

Analysis of PDEs · Mathematics 2018-11-26 Andrea Signori

We study a stochastic phase-field model for tumor growth dynamics coupling a stochastic Cahn-Hilliard equation for the tumor phase parameter with a stochastic reaction-diffusion equation governing the nutrient proportion. We prove strong…

Analysis of PDEs · Mathematics 2021-01-19 Carlo Orrieri , Elisabetta Rocca , Luca Scarpa

A distributed optimal control problem for a diffuse interface model, which physical context is that of tumour growth dynamics, is addressed. The system we deal with comprises a Cahn--Hilliard equation for the tumour fraction coupled with a…

Analysis of PDEs · Mathematics 2021-01-20 Andrea Signori

In this paper, a distributed optimal control problem is studied for a diffuse interface model of tumor growth which was proposed in [A. Hawkins-Daruud, K.G. van der Zee, J.T. Oden, Numerical simulation of a thermodynamically consistent…

Analysis of PDEs · Mathematics 2018-09-10 Pierluigi Colli , Gianni Gilardi , Elisabetta Rocca , Jürgen Sprekels

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 models the growth of a tumor in the presence of a nutrient…

Optimization and Control · Mathematics 2016-08-02 Harald Garcke , Kei-Fong Lam , Elisabetta Rocca

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…

Optimization and Control · Mathematics 2021-10-12 Matthias Ebenbeck , Patrik Knopf
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