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This paper is concerned with a boundary control problem for the Cahn--Hilliard equation coupled with dynamic boundary conditions. In order to handle the control problem, we restrict our analysis to the case of regular potentials defined on…

Analysis of PDEs · Mathematics 2021-01-20 Pierluigi Colli , Andrea Signori

This work addresses an optimal control problem constrained by a degenerate kinetic equation of parabolic-hyperbolic type. Using a hypocoercivity framework we establish the well-posedness of the problem and demonstrate that the optimal…

Numerical Analysis · Mathematics 2024-12-17 Aaron Pim , Tristan Pryer , Alex Trenam

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

We consider a heat conduction problem $S$ with mixed boundary conditions in a $n$-dimensional domain $\Omega$ with regular boundary and a family of problems $S_{\alpha}$ with also mixed boundary conditions in $\Omega$, where $\alpha>0$ is…

Optimization and Control · Mathematics 2021-03-30 C. M. Bollo , C. M. Gariboldi , D. A. Tarzia

We study a control problem where the state equation is a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise. We allow the control to act on the boundary and set stochastic boundary…

Probability · Mathematics 2025-11-26 Stefano Bonaccorsi , Adrian Zalinescu

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

We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced…

Optimization and Control · Mathematics 2025-10-17 Michael Kartmann , Stefan Volkwein

A boundary control problem for the pure 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 equation,…

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

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 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

Relying on the careful study of a related problem in the calculus of variations, we study a class of optimal control problems in which the control lies on the acceleration, with state constraints on the position variable. In dimension one,…

Optimization and Control · Mathematics 2025-10-10 Yves Achdou

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

We consider a heat conduction problem $S$ with mixed boundary conditions in a n-dimensional domain $\Omega$ with regular boundary $\Gamma$ and a family of problems $S_{\alpha}$, where the parameter $\alpha>0$ is the heat transfer…

Optimization and Control · Mathematics 2019-12-20 Domingo A. Tarzia , Carolina M. Bollo , Claudia M. Gariboldi

We derive existence results and first order necessary optimality conditions for optimal control problems governed by quasilinear parabolic PDEs with a class of first order nonlinearities that include for instance quadratic gradient terms.…

Optimization and Control · Mathematics 2025-07-03 Lucas Bonifacius , Fabian Hoppe , Hannes Meinlschmidt , Ira Neitzel

We present a branch-and-bound algorithm for globally solving parabolic optimal control problems with binary switches that have bounded variation and possibly need to satisfy further combinatorial constraints. More precisely, for a given…

Optimization and Control · Mathematics 2024-01-19 Christoph Buchheim , Alexandra Grütering , Christian Meyer

Controlling the shape and position of moving and pinned droplets on a solid surface is an important feature often found in microfluidic applications. In this work, we consider a well investigated phase field model including contact line…

Numerical Analysis · Mathematics 2020-02-10 Henning Bonart , Christian Kahle

This work concentrates on a class of optimal control problems for semilinear parabolic equations subject to control constraint of the form $\|u(t)\|_{L^1(\Omega)} \le \gamma$ for $t \in (0,T)$. This limits the total control that can be…

Optimization and Control · Mathematics 2021-12-03 Eduardo Casas , Karl Kunisch

In this paper, we study an optimal boundary control problem for a model for phase separation taking place in a spatial domain that was introduced by Podio-Guidugli in Ric. Mat. 55 (2006), pp. 105-118. The model consists of a strongly…

Analysis of PDEs · Mathematics 2017-09-08 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

A class of optimal control problems of hybrid nature governed by semilinear parabolic equations is considered. These problems involve the optimization of switching times at which the dynamics, the integral cost, and the bounds on the…

Optimization and Control · Mathematics 2016-11-30 Sébastien Court , Karl Kunisch , Laurent Pfeiffer

The paper addresses the study of a class of evolutionary quasi-variational inequalities of the parabolic type arising in the formation and growth models of granular and cohensionless materials. Such models and their mathematical…

Optimization and Control · Mathematics 2022-09-02 Harbir Antil , Rafael Arndt , Boris S. Mordukhovich , Dao Nguyen , Carlos N. Rautenberg