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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 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

We study an optimal control problem for a stochastic model of tumour growth with drug application. This model consists of three stochastic hyperbolic equations describing the evolution of tumour cells. It also includes two stochastic…

Optimization and Control · Mathematics 2024-08-30 Sakine Esmaili , M. R. Eslahchi , Delfim F. M. Torres

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 paper we study the optimal control of an initial-boundary value problem for the classical nonviscous Cahn-Hilliard system with zero Neumann boundary conditions. Phase field systems of this type govern the evolution of diffusive…

Optimization and Control · Mathematics 2024-06-12 Pierluigi Colli , 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

In this paper we study the optimal control of a parabolic initial-boundary value problem of viscous Cahn-Hilliard type with zero Neumann boundary conditions. Phase field systems of this type govern the evolution of diffusive phase…

Optimization and Control · Mathematics 2024-09-20 Pierluigi Colli , Jürgen Sprekels , Fredi Tröltzsch

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

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

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

We introduce a new diffuse interface model for tumour growth in the presence of a nutrient, in which we take into account mechanical effects and reversible tissue damage. The highly nonlinear PDEs system mainly consists of a Cahn-Hilliard…

Analysis of PDEs · Mathematics 2025-10-09 Giulia Cavalleri

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

We investigate a distributed optimal control problem for a nonlocal phase field model of viscous Cahn-Hilliard type. The model constitutes a nonlocal version of a model for two-species phase segregation on an atomic lattice under the…

Analysis of PDEs · Mathematics 2016-09-19 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

A new class of cost functionals for optimal control of quantum systems which produces controls which are sparse in frequency and smooth in time is proposed. This is achieved by penalizing a suitable time-frequency representation of the…

Optimization and Control · Mathematics 2016-07-15 Gero Friesecke , Felix Henneke , Karl Kunisch

We provide an overview of an optimal control problem within a stochastic model of tumor growth, which includes drug application. The model comprises two stochastic differential equations (SDE) representing the diffusion of nutrient and drug…

Optimization and Control · Mathematics 2024-11-12 Noelymar Farinacci

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 propose and study a spatial diffusion model for the control of anthracnose disease in a bounded domain. The model is a generalization of the one previously developed in [14]. We use the model to simulate two different types…

Optimization and Control · Mathematics 2016-08-08 David Jaurès Fotsa Mbogne , Christopher Thron

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

This paper is concerned with a phase field system of Cahn-Hilliard type that is related to a tumor growth model and consists of three equations in terms of the variables order parameter, chemical potential and nutrient concentration. This…

Analysis of PDEs · Mathematics 2015-03-04 Pierluigi Colli , Gianni Gilardi , Elisabetta Rocca , Jürgen Sprekels

We address an optimal control problem governed by a system coupling a Brinkman-type momentum equation for the velocity field with a sixth-order Cahn-Hilliard equation for the phase variable, incorporating curvature effects in the free…

Optimization and Control · Mathematics 2026-01-12 Pierluigi Colli , Gianni Gilardi , Andrea Signori , Jürgen Sprekels