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In this paper, we study initial-boundary value problems for the Cahn--Hilliard system with convection and nonconvex potential, where dynamic boundary conditions are assumed for both the associated order parameter and the corresponding…

Optimization and Control · Mathematics 2018-03-15 Gianni Gilardi , 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

This article discusses an optimal control problem for a phase field model of two immiscible incompressible fluid flow, incorporating surface tension effects. The optimal control problem is defined with a $L^2$-cost functional and subject to…

Optimization and Control · Mathematics 2026-05-12 Arghya Kundu

The Cahn-Hilliard equation is a fundamental model that describes the phase separation process in multi-component mixtures. It has been successfully extended to many different contexts in several scientific fields. In this survey article, we…

Analysis of PDEs · Mathematics 2022-06-22 Hao Wu

In this work, we study an optimal boundary control problem for a Cahn - Hilliard -Navier-Stokes (CHNS) system in a two dimensional bounded domain. The CHNS system consists of a Navier-Stokes equation governing the fluid velocity field…

Optimization and Control · Mathematics 2024-05-17 Manika Bag , Tania Biswas , Sheetal Dharmatti

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 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

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

We consider local and nonlocal Cahn-Hilliard equations with constant mobility and singular potentials including, e.g., the Flory-Huggins potential, subject to no-flux (or periodic) boundary conditions. The main goal is to show that the…

Analysis of PDEs · Mathematics 2025-05-28 Maurizio Grasselli , Luca Scarpa , Andrea Signori

An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of…

Optimization and Control · Mathematics 2010-08-20 Hongwei Lou

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 class of closed loop stochastic optimal control problems in finite time horizon, in which the cost is an expectation conditional on the event that the process has not exited a given bounded domain. An important difficulty is…

Optimization and Control · Mathematics 2019-12-19 Yves Achdou , Mathieu Laurière , Pierre-Louis Lions

We consider a class of Cahn-Hilliard equation that characterizes phase separation phenomena of binary mixtures in a bounded domain $\Omega \subset \mathbb{R}^d$ $(d\in \{2,3\})$ with non-permeable boundary. The equations in the bulk are…

Analysis of PDEs · Mathematics 2024-06-03 Maoyin Lv , Hao Wu

A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…

Optimization and Control · Mathematics 2022-11-24 Bui Trong Kien , Bui Ngoc Muoi , Ching-Feng Wen , Jen-Chih Yao

In this paper, we consider a class of optimal control problems governed by 1D parabolic state-systems of KWC types with dynamic boundary conditions. The state-systems are based on a phase-field model of grain boundary motion, proposed in…

Analysis of PDEs · Mathematics 2020-10-05 Shodai Kubota , Ryota Nakayashiki , Ken Shirakawa

The Cahn--Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In recent years, several types of dynamic boundary conditions have been proposed in order to account for possible short-range…

Analysis of PDEs · Mathematics 2023-07-28 Chun Liu , Hao Wu

We prove well-posedness results for the solution to an initial and boundary-value problem for an Allen-Cahn type equation describing the phenomenon of phase transitions for a material contained in a bounded and regular domain. The dynamic…

Analysis of PDEs · Mathematics 2012-06-29 Luca Calatroni , Pierluigi Colli

An asymptotic analysis for a system with equation and dynamic boundary condition of Cahn-Hilliard type is carried out as the coefficient of the surface diffusion acting on the phase variable tends to 0, thus obtaining a forward-backward…

Analysis of PDEs · Mathematics 2021-06-03 Pierluigi Colli , Takeshi Fukao , Luca Scarpa

In the paper we consider the infinite horizon control problems on the interval with free right-hand endpoint. We obtain the necessary conditions of strict optimality. The method of the proof actually follows the classic paper by Halkin, and…

Optimization and Control · Mathematics 2013-01-01 Dmitry Khlopin

We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…

Probability · Mathematics 2008-12-20 Seid Bahlali