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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 nonlocal-to-local asymptotics for a tumor-growth model coupling a viscous Cahn-Hilliard equation describing the tumor proportion with a reaction-diffusion equation for the nutrient phase parameter. First, we prove…

Analysis of PDEs · Mathematics 2023-11-20 Elisa Davoli , Elisabetta Rocca , Luca Scarpa , Lara Trussardi

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

We consider a particular phase field system which physical context is that of tumor growth dynamics. The model we deal with consists of a Cahn-Hilliard type equation governing the evolution of the phase variable which takes into account the…

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

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

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

We investigate the long-time dynamics and optimal control problem of a diffuse interface model that describes the growth of a tumor in presence of a nutrient and surrounded by host tissues. The state system consists of a Cahn-Hilliard type…

Analysis of PDEs · Mathematics 2023-07-28 Cecilia Cavaterra , Elisabetta Rocca , Hao Wu

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

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

This paper presents a mathematical framework for optimizing drug delivery in cancer treatment using a nonlocal model of solid tumor growth. We present a coupled system of partial differential equations that incorporate long-range cellular…

Optimization and Control · Mathematics 2025-03-13 Bouhamidi Abderrahman , El Harraki Imad , Melouani Yassine

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, 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

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

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 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

We study a distributed optimal control problem for a nonisothermal Caginalp-type phase-field model that describes tumour growth under thermal therapy. The PDE system couples a possibly viscous Cahn-Hilliard equation, governing the evolution…

Optimization and Control · Mathematics 2026-05-05 Giulia Cavalleri , Pierluigi Colli , Elisabetta Rocca

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 address a distributed control problem for a system of partial differential equations describing the evolution of a tumor that takes the biological mechanism of chemotaxis into account. The system describing the evolution…

Optimization and Control · Mathematics 2023-09-19 Gianni Gilardi , Andrea Signori , Jürgen Sprekels

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
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