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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

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

The Cauchy problem is studied for very general systems of evolution equations, where the time derivative of solution is written by Fourier multipliers in space and analytic nonlinearity, with no other structural requirement. We construct a…

Analysis of PDEs · Mathematics 2024-01-19 Kenji Nakanishi , Baoxiang Wang

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

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

Optimal Dirichlet boundary control for a fractional/normal evolution with a final observation is considered. The unique existence of the solution and the first-order optimality condition of the optimal control problem are derived. The…

Numerical Analysis · Mathematics 2020-07-20 Qin Zhou , Binjie Li

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 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

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

The well-posedness of a class of optimal control problems is analysed, where the state equation couples a nonlinear degenerate Fokker-Planck equation with a system of Ordinary Differential Equations (ODEs). Such problems naturally arise as…

Optimization and Control · Mathematics 2024-11-01 Francesca Anceschi , Giacomo Ascione , Daniele Castorina , Francesco Solombrino

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

This paper is concerned with an optimal control problem governed by nonsmooth semilinear elliptic partial differential equations with both distributed and boundary unilateral pointwise control constraints, in which the nonlinear coefficient…

Optimization and Control · Mathematics 2025-01-28 Vu Huu Nhu , Nguyen Hai Son

In this paper we study optimal control problem for non local Cahn-Hilliard-Brinkman system which models phase separation of binary fluids in porous media. We consider the system in two dimensional bounded domain with regular potential. We…

Analysis of PDEs · Mathematics 2019-11-11 Sheetal Dharmatti , Mahendranath PL N

In this paper, we study an optimal control problem for a viscous Cahn--Hilliard system with zero Neumann boundary conditions in which a hyperbolic relaxation term involving the second time derivative of the chemical potential has been added…

Optimization and Control · Mathematics 2025-03-27 Pierluigi Colli , Jürgen Sprekels

This paper treats a distributed optimal control problem for a tumor growth model of Cahn-Hilliard type including chemotaxis. The evolution of the tumor fraction is governed by a variational inequality corresponding to a double obstacle…

Optimization and Control · Mathematics 2021-04-21 Pierluigi Colli , Andrea Signori , 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

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

Despite the strong focus of regularization on ill-posed problems, the general construction of such methods has not been fully explored. Moreover, many previous studies cannot be clearly adapted to handle more complex scenarios, albeit the…

Analysis of PDEs · Mathematics 2016-10-20 Nguyen Huy Tuan , Vo Anh Khoa , Vo Van Au

In this contribution, we study an optimal control problem for the celebrated nonlocal Cahn-Hilliard equation endowed with the singular Flory-Huggins potential in the three-dimensional setting. The control enters the governing state system…

Optimization and Control · Mathematics 2024-01-19 Andrea Poiatti , Andrea Signori

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 generalized and relaxed version…

Analysis of PDEs · Mathematics 2019-08-29 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels