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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

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

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

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

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 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

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 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

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

We investigate a distributed optimal control problem for a phase field model of Cahn-Hilliard type. The model describes two-species phase segregation on an atomic lattice under the presence of diffusion; it has been recently introduced by…

Analysis of PDEs · Mathematics 2015-05-28 Pierluigi Colli , Gianni Gilardi , Paolo Podio-Guidugli , Jürgen Sprekels

We study the optimal control problem of a free boundary PDE model describing the growth of multilayered tumor tissue in vitro. We seek the optimal amount of tumor growth inhibitor that simultaneously minimizes the thickness of the tumor…

Analysis of PDEs · Mathematics 2024-10-21 Xinyue Evelyn Zhao , Yixiang Wu , Rachel Leander , Wandi Ding , Suzanne Lenhart

In this paper we consider an optimal control problem arising from a chemotherapeutic drug treatment for tumor cells in a living tissue. The mathematical model for the interaction of chemotherapeutic drug and the normal, tumor and immune…

Analysis of PDEs · Mathematics 2022-12-13 Hong-Ming Yin

This paper is concerned with a distributed optimal control problem for a nonlocal phase field model of Cahn-Hilliard type, which is a nonlocal version of a model for two-species phase segregation on an atomic lattice under the presence of…

Analysis of PDEs · Mathematics 2016-07-08 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

In this paper, we investigate a distributed optimal control problem for a convective viscous Cahn-Hilliard system with dynamic boundary conditions. Such systems govern phase separation processes between two phases taking place in an…

Analysis of PDEs · Mathematics 2017-09-08 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

In this paper, we study an optimal control problem for a coupled non-linear system of reaction-diffusion equations with degenerate diffusion, consisting of two partial differential equations representing the density of cells and the…

Optimization and Control · Mathematics 2024-07-11 Georges Chamoun , Mazen Saad , Toni Sayah , Sarah Serhal

In this paper we study a distributed control problem for a phase-field system of conserved type with a possibly singular potential. We mainly handle two cases: the case of a viscous Cahn-Hilliard type dynamics for the phase variable in case…

Analysis of PDEs · Mathematics 2017-09-12 P. Colli , G. Gilardi , G. Marinoschi , E. Rocca

In this paper, we study an optimal control problem for a brain tumor growth model that incorporates lactate metabolism, viscoelastic effects, and tissue damage. The PDE system, introduced in [G. Cavalleri, P. Colli, A. Miranville, E. Rocca,…

Analysis of PDEs · Mathematics 2025-03-24 Giulia Cavalleri , Alain Miranville

In the present work, we develop a comprehensive and rigorous analytical framework for a non-local phase-field model that describes tumour growth dynamics. The model is derived by coupling a non-local Cahn-Hilliard equation with a parabolic…

Analysis of PDEs · Mathematics 2025-03-14 Maurizio Grasselli , Luca Melzi , Andrea Signori

This paper provides a unified mathematical analysis of a family of non-local diffuse interface models for tumor growth describing evolutions driven by long-range interactions. These integro-partial differential equations model cell-to-cell…

Analysis of PDEs · Mathematics 2021-07-07 Luca Scarpa , Andrea Signori

In this paper we study a distributed optimal control problem for a nonlocal convective Cahn--Hilliard equation with degenerate mobility and singular potential in three dimensions of space. While the cost functional is of standard tracking…

Analysis of PDEs · Mathematics 2014-09-26 Elisabetta Rocca , Juergen Sprekels