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This paper is concerned with the constrained approximate null controllability of heat equation coupled by a real matrix $P$, where the controls are impulsive and periodically acted into the system through a series of real matrices…

Optimization and Control · Mathematics 2020-05-18 Lijuan Wang , Qishu Yan , Huaiqiang Yu

We investigate $C^1$ finite element methods for one dimensional elliptic distributed optimal control problems with pointwise constraints on the derivative of the state formulated as fourth order variational inequalities for the state…

Numerical Analysis · Mathematics 2020-06-29 Susanne C. Brenner , Li-Yeng Sung , Winnifried Wollner

For a heat equation with Robin's boundary conditions which depends on a parameter $\alpha>0$, we prove that its unique weak solution $\rho^\alpha$ converges, when $\alpha$ goes to zero or to infinity, to the unique weak solution of the heat…

Probability · Mathematics 2013-03-26 Tertuliano Franco , Patricia Gonçalves , Adriana Neumann

We consider parabolic equations on bounded smooth open sets $\Om\subset \R^N$ ($N\ge 1$) with mixed Dirichlet type boundary-exterior conditions associated with the elliptic operator $\mathscr{L} \coloneqq - \Delta + (-\Delta)^{s}$…

Analysis of PDEs · Mathematics 2022-02-28 Jean-Daniel Djida , Gisele Mophou , Mahamadi Warma

In this paper, we are concerned with the boundary controllability of heat equation with dynamic boundary conditions. More precisely, we prove that the equation is null controllable at any positive time by means of a boundary control…

Analysis of PDEs · Mathematics 2022-06-23 S. E. Chorfi , G. El Guermai , A. Khoutaibi , L. Maniar

This paper presents a new method for solving a class of nonlinear optimal control problems with a quadratic performance index. In this method, first the original optimal control problem is transformed into a nonlinear two-point boundary…

Optimization and Control · Mathematics 2014-09-18 Amin Jajarmi , Hamidreza Ramezanpour , Arman Sargolzaei , Pouyan Shafaei

The article examines a linear-quadratic Neumann control problem that is governed by a non-coercive elliptic equation. Due to the non-self-adjoint nature of the linear control-to-state operator, it is necessary to independently study both…

Optimization and Control · Mathematics 2025-06-25 Thomas Apel , Mariano Mateos , Arnd Rösch

A boundary control problem for the following generalized Korteweg-de Vries-Burgers-Huxley equation: $$u_t=\nu u_{xx}-\mu u_{xxx}-\alpha u^{\delta}u_x+\beta u(1-u^{\delta})(u^{\delta}-\gamma), \ x\in[0,1], \ t>0,$$ where…

Analysis of PDEs · Mathematics 2024-02-06 Manil T. Mohan , Shri Lal Raghudev Ram Singh

In this paper, we introduce a novel pseudospectral method for the numerical solution of optimal control problems governed by a parabolic distributed parameter system. The infinite-dimensional optimal control problem is reduced into a…

Optimization and Control · Mathematics 2023-03-06 Kareem T. Elgindy

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

We consider initial-boundary value problems (IBVPs) on a finite interval for the system of the energy balance equation and Guyer-Krumhansl constitutive equation. Boundary conditions comprise various models of behavior of a physical system…

Analysis of PDEs · Mathematics 2025-12-01 Sergey A. Rukolaine

This paper is concerned with the optimal control problem governed by a linear parabolic equation and subjected to box constraints on control variables. This type of problem has important applications in heating and cooling systems. By…

Optimization and Control · Mathematics 2022-04-04 Hailing Wang , Changjun Yu , Di Wu

We consider the homogenization of an optimal control problem in which the control is placed on a part of the boundary and the spatial domain contains a thin layer of "small particles", very close to the controlling boundary, and a Robin…

Analysis of PDEs · Mathematics 2022-01-03 J. I. Díaz , A. V. Podolskiy , T. A. Shaposhnikova

Controlling the growth of material damage is an important engineering task with plenty of real world applications. In this paper we approach this topic from the mathematical point of view by investigating an optimal boundary control problem…

Optimization and Control · Mathematics 2016-06-20 M. Hassan Farshbaf-Shaker , Christian Heinemann

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

This paper studies the existence of solutions and, in particular, the well-posedness of a class of boundary control systems. Our main result provides explicit and verifiable conditions on the system data that guarantee continuous dependence…

Optimization and Control · Mathematics 2026-03-13 Yassine El Gantouh , Jun Zheng , Guchuan Zhu

We examine the minimization of a quadratic cost functional composed of the output and the final state of abstract infinite-dimensional evolution equations in view of existence of solutions and optimality conditions. While the initial value…

Optimization and Control · Mathematics 2024-12-20 Timo Reis , Manuel Schaller

The aim of this work is to present some strategies to solve numerically controllability problems for the two-dimensional heat equation, the Stokes equations and the Navier-Stokes equations with Dirichlet boundary conditions. The main idea…

Optimization and Control · Mathematics 2024-02-12 Enrique Fernández-Cara , Arnaud Münch , Diego A. Souza

In this note, we consider an optimal control problem associated to a differential equation driven by a H\"{o}lder continuous function g of index greater than 1/2. We split our study in two cases. If the coefficient of dg\_t does not depend…

Probability · Mathematics 2007-05-23 Laurent Mazliak , Ivan Nourdin

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