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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

We address the problem of controllability of the MHD system in a rectangular domain with a control prescribed on the side boundary. We identify a necessary and sufficient condition on the data to be null controllable, i.e., can be driven to…

Analysis of PDEs · Mathematics 2021-08-30 Igor Kukavica , Matthew Novack , Vlad Vicol

This work represents a first contribution on the problem of boundary stabilization for the phase field system of Cahn-Hilliard type, which models the phase separation in a binary mixture. The feedback controller we design here is with…

Analysis of PDEs · Mathematics 2018-12-03 Pierluigi Colli , Gianni Gilardi , Ionut Munteanu

The Cahn--Hilliard equation is one of the most common models to describe phase separation processes of a mixture of two materials. For a better description of short-range interactions between the material and the boundary, various dynamic…

Analysis of PDEs · Mathematics 2021-04-27 Patrik Knopf , Kei Fong Lam , Chun Liu , Stefan Metzger

A distributed optimal control problem for a phase field system which physical context is that of tumor growth is discussed. The system we are going to take into account consists of a Cahn-Hilliard equation for the phase variable (relative…

Analysis of PDEs · Mathematics 2021-01-20 Andrea Signori

This paper provides necessary conditions of optimality for optimal control problems with time delays in both state and control variables. Different versions of the necessary conditions cover fixed end-time problems and, under additional…

Dynamical Systems · Mathematics 2017-01-09 Andrea Boccia , Richard B. Vinter

We consider a controlled state equation of parabolic type on the halfline $(0,+\infty)$ with boundary conditions of Dirichlet type in which the unknown is equal to the sum of the control and of a white noise in time. We study finite horizon…

Probability · Mathematics 2013-04-10 Federica Masiero

We study the problem of state transition on a finite time interval with minimal energy supply for linear port-Hamiltonian systems. While the cost functional of minimal energy supply is intrinsic to the port-Hamiltonian structure, the…

Optimization and Control · Mathematics 2023-11-21 Timm Faulwasser , Jonas Kirchhoff , Volker Mehrmann , Friedrich Philipp , Manuel Schaller , Karl Worthmann

Problems for partial differential equations coupled with dynamic boundary conditions can be viewed as a type of transmission problem between the bulk and its boundary. For the heat equation and the Allen-Cahn equation, various forms of such…

Analysis of PDEs · Mathematics 2025-08-06 Pierluigi Colli , Takeshi Fukao

The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets…

Optimization and Control · Mathematics 2021-03-17 Tan H. Cao , Giovanni Colombo , Boris S. Mordukhovich , Dao Nguyen

A class of optimal control problems governed by semilinear parabolic equations with mixed constraints and a box constraint for control variable is considered. We show that if the separation condition is satisfied, then both optimality…

Optimization and Control · Mathematics 2023-09-06 Huynh Khanh , Bui Trong Kien

In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed…

Portfolio Management · Quantitative Finance 2014-06-27 Xiongfei Jian , Xun Li , Fahuai Yi

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 work addresses the problem of solving the Cahn-Hilliard equation numerically. For that we introduce an abstract formulation for Cahn-Hilliard type equations with dynamic boundary conditions, we conduct the spatial semidiscretization…

Numerical Analysis · Mathematics 2022-08-09 Paula Harder

The purpose of this work is the formulation of optimality conditions for phase-field optimal control problems. The forward problem is first stated as an abstract nonlinear optimization problem, and then the necessary optimality conditions…

Optimization and Control · Mathematics 2023-10-06 Denis Khimin , Johannes Lankeit , Marc C. Steinbach , Thomas Wick

We extend the Boltzmann-Hamel equations to the optimal control setting, producing a set of equations for both kinematic and dynamic nonholonomic optimal control problems. In particular, we will show the dynamic optimal control problem can…

Optimization and Control · Mathematics 2007-07-03 Jared M. Maruskin , Anthony M. Bloch

We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…

Probability · Mathematics 2008-12-20 Seid Bahlali

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

In this paper we focus on the Cahn-Hilliard equation with dynamic boundary conditions, by adding two hyperbolic relaxation terms to the system. We verify that the energy of the total system is decreasing with time. By adding two…

Numerical Analysis · Mathematics 2025-04-03 Minghui Yu , Rui Chen

This paper studies a kind of minimal time control problems related to the exact synchronization for a controlled linear system of parabolic equations. Each problem depends on two parameters: the bound of controls and the initial state. The…

Optimization and Control · Mathematics 2018-03-02 Lijuan Wang , Qishu Yan