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In this paper, we study an insulation problem that seeks to determine the optimal distribution of a given amount $m>0$ of insulating material coating an insulated boundary part $\Gamma_I\subseteq \partial\Omega$ of a thermally conducting…

Analysis of PDEs · Mathematics 2025-12-16 Harbir Antil , Alex Kaltenbach , Keegan L. A. Kirk

Dynamic phenomena in social and biological sciences can often be modeled by employing reaction-diffusion equations. When addressing the control of these modes, from a mathematical viewpoint one of the main challenges is that, because of the…

Optimization and Control · Mathematics 2020-06-02 Domènec Ruiz-Balet , Enrique Zuazua

An optimal control of a steady state thermistor problem is considered, where the convective boundary coefficient is taken as the control variable. A distinctive feature of this paper is that the problem is considered in arbitrary…

Optimization and Control · Mathematics 2019-02-06 Volodymyr Hrynkiv , Sergiy Koshkin

We study thermal insulating of a bounded body $\Omega\subset \mathbb{R}^n$. Under a prescribed heat source $f\geq 0$, we consider a model of heat transfer between $\Omega$ and the environment determined by convection; this corresponds,…

Analysis of PDEs · Mathematics 2020-08-06 Francesco Della Pietra , Carlo Nitsch , Riccardo Scala , Cristina Trombetti

We investigate optimal control problems governed by the elliptic partial differential equation $-\Delta u=f$ subject to Dirichlet boundary conditions on a given domain $\Omega$. The control variable in this setting is the right-hand side…

Optimization and Control · Mathematics 2025-09-03 Giuseppe Buttazzo , Juan Casado-Díaz , Faustino Maestre

We study Dirichlet boundary control of Stokes flows in 2D polygonal domains. We consider cost functionals with two different boundary control regularization terms: the $L^2$ norm and an energy space seminorm. We prove well-posedness and…

Optimization and Control · Mathematics 2020-11-18 W. Gong , M. Mateos , J. Singler , Y. Zhang

In this paper, we study an insulation problem that seeks the optimal distribution of a fixed amount $m>0$ of insulating material coating an insulated boundary $\Gamma_I\subseteq \partial\Omega$ of a thermally conducting body…

Analysis of PDEs · Mathematics 2025-08-04 Harbir Antil , Alex Kaltenbach , Keegan L. A. Kirk

This paper is concerned with an optimal control problem subject to the $H^1$-critical defocusing semilinear wave equation on a smooth and bounded domain in three spatial dimensions. Due to the criticality of the nonlinearity in the wave…

Optimization and Control · Mathematics 2019-07-08 Karl Kunisch , Hannes Meinlschmidt

We study the optimal control of a steady-state dead oil isotherm problem. The problem is described by a system of nonlinear partial differential equations resulting from the traditional modelling of oil engineering within the framework of…

Optimization and Control · Mathematics 2013-10-03 Moulay Rchid Sidi Ammi , Agnieszka B. Malinowska , Delfim F. M. Torres

A heat exchanger can be modeled as a closed domain containing an incompressible fluid. The moving fluid has a temperature distribution obeying the advection-diffusion equation, with zero temperature boundary conditions at the walls.…

Fluid Dynamics · Physics 2018-02-23 Florence Marcotte , Charles R. Doering , Jean-Luc Thiffeault , William R. Young

We consider a bounded domain D whose regular boundary consists of the union of two portions F1 and F2. The convergence of a family of continuous Neumann boundary mixed elliptic optimal control problems (Pa), governed by elliptic variational…

Numerical Analysis · Mathematics 2014-12-22 Domingo A. Tarzia

In the paper, the problems of approximate controllability are studied for the control system $w_t=\Delta w$, $w(0,x_2,t)=u(x_2,t)$, $x_1\in\mathbb R_+=(0,+\infty)$, $x_2\in\mathbb R$, $t\in(0,T)$, where $u$ is a control belonging to a…

Optimization and Control · Mathematics 2025-06-13 Larissa Fardigola , Kateryna Khalina

We consider an optimal control problem on a bounded domain $\Omega\subset\mathbb{R}^2,$ governed by a parabolic convection--diffusion--reaction equation with pointwise control constraints. We follow the optimize--then--discretize approach,…

Numerical Analysis · Mathematics 2025-12-11 Christos Pervolianakis

The main aim of this paper is to provide a new feedback law for the heat equations in a bounded domain $\Omega $ with Dirichlet boundary condition. Two constraints will be compulsory: First, The controls are active in a subdomain of $\Omega…

Analysis of PDEs · Mathematics 2016-12-01 Kim Dang Phung , Gengsheng Wang , Yashan Xu

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

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

We consider the steady heat transfer between a collection of impermeable obstacles immersed in an incompressible 2D potential flow, when each obstacle has a prescribed boundary temperature distribution. Inside the fluid, the temperature…

Fluid Dynamics · Physics 2025-09-12 Kyle McKee , Keaton Burns

In this paper, we study the impulse controllability of a multi-dimensional heat equation with dynamic boundary conditions in a bounded smooth domain. Using a recent approach based on finite-time stabilization, we show that the system is…

Optimization and Control · Mathematics 2023-10-31 Salah-Eddine Chorfi , Ghita El Guermai , Lahcen Maniar , Walid Zouhair

The aim of this work is to give a broad panorama of the control properties of fractional diffusive models from a numerical analysis and simulation perspective. We do this by surveying several research results we obtained in the last years,…

Analysis of PDEs · Mathematics 2021-10-19 Umberto Biccari , Mahamadi Warma , Enrique Zuazua

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