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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 2017-09-13 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

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 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 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

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

We consider a non-local tumour growth model of phase-field type, describing the evolution of tumour cells through proliferation in presence of a nutrient. The model consists of a coupled system, incorporating a non-local Cahn-Hilliard…

Analysis of PDEs · Mathematics 2024-07-29 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 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, 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 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 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 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

The paper arXiv:1804.11290 contains well-posedness and regularity results for a system of evolutionary operator equations having the structure of a Cahn-Hilliard system. The operators appearing in the system equations were fractional…

Analysis of PDEs · Mathematics 2018-12-17 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

This paper is concerned with the distributed optimal control of a time-discrete Cahn--Hilliard/Navier--Stokes system with variable densities. It focuses on the double-obstacle potential which yields an optimal control problem for a family…

Analysis of PDEs · Mathematics 2015-06-12 Michael Hintermüller , Tobias Keil , Donat Wegner

Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…

Optimization and Control · Mathematics 2018-02-13 Laurent Pfeiffer

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

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

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

In this work, we investigate optimal control of a Brinkman equation couple with sixth-order Cahn-Hilliard equation. The Cahn-Hilliard equation is endowed with a source term accounting for mass exchange and the velocity equation contains a…

Optimization and Control · Mathematics 2025-12-09 Manika Bag

In this paper, we study a system of three evolutionary operator equations involving fractional powers of selfadjoint, monotone, unbounded, linear operators having compact resolvents. This system constitutes a generalization of a phase field…

Analysis of PDEs · Mathematics 2019-06-27 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels