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Related papers: Exact Controllability for a Schr\"odinger equation…

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This paper is addressed to studying the exact controllability for stochastic transport equations by two controls: one is a boundary control imposed on the drift term and the other is an internal control imposed on the diffusion term. By…

Optimization and Control · Mathematics 2013-10-22 Qi Lü

In this paper, we study the exact boundary controllability of the linear Biharmonic Schr\"odinger equation $i\partial_ty=-\partial_x^4y+ \gamma\partial_x^2y$ on a bounded domain with hinged boundary conditions and boundary control acts on…

Analysis of PDEs · Mathematics 2022-04-27 Kaïs Ammari , Hedi Bouzidi

In [15] we proposed a set of sufficient conditions for the approximate controllability of a discrete-spectrum bilinear Schr\"odinger equation. These conditions are expressed in terms of the controlled potential and of the eigenpairs of the…

Optimization and Control · Mathematics 2010-09-27 Paolo Mason , Mario Sigalotti

Motivated by various applications, this article develops the notion of boundary control for Maxwell's equations in the frequency domain. Surface curl is shown to be the appropriate regularization in order for the optimal control problem to…

Optimization and Control · Mathematics 2022-10-03 Harbir Antil , Hugo Díaz

We consider a fully-discrete approximations of 1-D heat equation with dynamic boundary conditions for which we provide a controllability result. The proof of this result is based on a relaxed observability inequality for the corresponding…

Analysis of PDEs · Mathematics 2022-09-30 Rodrigo Lecaros , Roberto Morales , Ariel Pérez , Sebastián Zamorano

We consider the 1D linear Schr{\"o}dinger equation, on a bounded interval, with Dirichlet boundary conditions and bilinear scalar control. The small-time local exact controllability around the ground state was proved in [BeaLau10], under an…

Analysis of PDEs · Mathematics 2021-07-20 Mégane Bournissou

A finite element analysis of a Dirichlet boundary control problem governed by the linear parabolic equation is presented in this article. The Dirichlet control is considered in a closed and convex subset of the energy space $H^1(\Omega…

Numerical Analysis · Mathematics 2021-11-04 Thirupathi Gudi , Gouranga Mallik , Ramesh Ch. Sau

We consider the linear heat equation with a Wentzell-type boundary condition and a Dirichlet control. Such a boundary condition can be reformulated as one of dynamic type. First, we formulate the boundary controllability problem of the…

Optimization and Control · Mathematics 2024-08-06 S. E. Chorfi , M. I. Ismailov , L. Maniar , I. Öner

This paper is concerned with the control properties of the Korteweg-de Vries (KdV) equation posed on a bounded interval with a distributed control. When the control region is an arbitrary open subdomain, we prove the null controllability of…

Analysis of PDEs · Mathematics 2021-05-03 Roberto Capistrano Filho , Ademir Pazoto , Lionel Rosier

Solutions of a system of wave equations are constructed for both homogeneous and inhomogeneous Dirichlet boundary conditions at every regularity level. We prove that boundary observability, and thus boundary exact controllability, at some…

Analysis of PDEs · Mathematics 2024-04-24 Thomas Perrin

We discuss the observability of a one-dimensional Schr\"odinger equation on certain time dependent domain. In linear moving case, we give the exact boundary and pointwise internal observability for arbitrary time. For the general moving, we…

Optimization and Control · Mathematics 2018-01-30 Duc-Trung Hoang

We study the boundary controllability problem for a multilayer Rao-Nakra sandwich beam. This beam model consists of a Rayleigh beam coupled with a number of wave equations. We consider all combinations of clamped and hinged boundary…

Analysis of PDEs · Mathematics 2014-05-20 A. Ozkan Ozer , Scott W. Hansen

This review examines classical and recent results on controllability and inverse problems for hyperbolic and dispersive equations with dynamic boundary conditions. We aim to illustrate the applicability of Carleman estimates to establish…

Optimization and Control · Mathematics 2025-05-22 S. E. Chorfi , L. Maniar , R. Morales

In the framework of the application of the Boundary Control method to solving the inverse dynamical problems for the one-dimensional Schr\"odinger and Dirac operators on the half-line and semi-infinite discrete Schr\"odinger operator, we…

Analysis of PDEs · Mathematics 2019-12-19 Alexander S. Mikhaylov , Victor S. Mikhaylov

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

We prove controllability of the Schr\"odinger equation in $\mathbb{R}^d$ in any time $T > 0$ with internal control supported on nonempty, periodic, open sets. This demonstrates in particular that controllability of the Schr\"odinger…

Analysis of PDEs · Mathematics 2023-03-13 Matthias Täufer

In this paper, we present a control problem related to a semilinear differential equation with a moving singularity, i.e., the singular point depends on a parameter. The particularity of the controllability condition resides in the fact…

Optimization and Control · Mathematics 2025-05-20 Radu Precup , Andrei Stan , Wei-Shih Du

The paper is devoted to the exact controllability of a system of coupled abstract wave equations when the control is exerted on a part of the boundary by means of one control. We give a Kalman type condition and give a description of the…

Analysis of PDEs · Mathematics 2020-01-06 Veli Shakhmurov

We study the boundary exact controllability for the quasilinear wave equation in the higher-dimensional case. Our main tool is the geometric analysis. We derive the existence of long time solutions near an equilibrium, prove the locally…

Analysis of PDEs · Mathematics 2007-05-23 Peng-Fei Yao

This article examines the Dirichlet boundary control problem governed by the Poisson equation, where the control variables are square integrable functions defined on the boundary of a two dimensional bounded, convex, polygonal domain. It…

Optimization and Control · Mathematics 2024-02-12 Sudipto Chowdhury , Divay Garg