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We study an optimal distributed control problem associated to a stochastic Cahn-Hilliard equation with a classical double-well potential and Wiener multiplicative noise, where the control is represented by a source-term in the definition of…

Optimization and Control · Mathematics 2020-01-07 Luca Scarpa

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

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

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

In this paper we study a distributed control problem for a phase field system of Caginalp type with logarithmic potential. The main aim of this work would be to force the location of the diffuse interface to be as close as possible to a…

Analysis of PDEs · Mathematics 2014-10-27 Pierluigi Colli , Gianni Gilardi , Gabriela Marinoschi , Elisabetta Rocca

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

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

A boundary control problem for the viscous Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first order necessary conditions for optimality are proved. Key words: Cahn-Hilliard…

Analysis of PDEs · Mathematics 2015-03-12 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

This paper proposes an optimal control problem for a parabolic equation with a nonlocal nonlinearity. The system is described by a parabolic equation involving a nonlinear term that depends on the solution and its integral over the domain.…

Optimization and Control · Mathematics 2024-03-20 Cyrille Kenne , Landry Djomegne , Gisèle Mophou

Existence and uniqueness are investigated for a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial…

Analysis of PDEs · Mathematics 2012-09-17 Pierluigi Colli , Gianni Gilardi , Paolo Podio-Guidugli , Jürgen Sprekels

We consider the optimal control of singular nonlinear partial differential equation which is the distributional formulation of the multiphase Stefan type free boundary problem for the general second order parabolic equation. Boundary heat…

Analysis of PDEs · Mathematics 2020-03-03 Ugur G. Abdulla , Evan Cosgrove

In this paper, we explore the solvability and the optimal control problem for a compartmental model based on reaction-diffusion partial differential equations describing a transmissible disease. The nonlinear model takes into account the…

Optimization and Control · Mathematics 2023-08-25 Pierluigi Colli , Gianni Gilardi , Gabriela Marinoschi

In the recent paper `Well-posedness and regularity for a generalized fractional Cahn-Hilliard system' (arXiv:1804.11290) by the same authors, general well-posedness results have been established for a a class of evolutionary systems of two…

Analysis of PDEs · Mathematics 2018-10-23 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

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

A Cahn-Hilliard equation with stochastic multiplicative noise and a random convection term is considered. The model describes isothermal phase-separation occurring in a moving fluid, and accounts for the randomness appearing at the…

Analysis of PDEs · Mathematics 2021-04-21 Luca Scarpa

In this paper we consider a nonlinear system of PDEs coupling the viscous Cahn-Hilliard-Oono equation with dynamic boundary conditions enjoying a similar structure on the boundary. After proving well-posedness of the corresponding initial…

Analysis of PDEs · Mathematics 2023-09-19 Gianni Gilardi , Elisabetta Rocca , Andrea Signori

We are concerned with a nonstandard phase field model of Cahn-Hilliard type. The model, which was introduced by Podio-Guidugli (Ric. Mat. 2006), describes two-species phase segregation and consists of a system of two highly nonlinearly…

Analysis of PDEs · Mathematics 2012-12-18 Pierluigi Colli , Gianni Gilardi , Pavel Krejčí , Jürgen Sprekels

This paper analyzes a discretization of a stochastic parabolic optimal control problem, where the diffusion term contains the control variable. With rough data, the convergence of the discretization is derived. In addition, a Monte-Carlo…

Numerical Analysis · Mathematics 2022-08-31 Binjie Li , Qin Zhou , Xiaoping Xie

We study some optimal control problems associated to the evolution of two isothermal, incompressible, immisible fluids in a two-dimensional bounded domain. The Cahn- Hilliard-Navier-Stokes model consists of a Navier-Stokes equation…

Analysis of PDEs · Mathematics 2019-03-20 Tania Biswas , Sheetal Dharmatti , Manil T Mohan

This paper investigates a nonlocal version of a model for phase separation on an atomic lattice that was introduced by P. Podio-Guidugli in Ric. Mat. 55 (2006) 105-118. The model consists of an initial-boundary value problem for a…

Analysis of PDEs · Mathematics 2015-11-16 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels