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Related papers: Internal null controllability for the one-dimensio…

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We discuss several new results on nonnegative approximate controllability for the one-dimensional Heat equation governed by either multiplicative or nonnegative additive control, acting within a proper subset of the space domain at every…

Optimization and Control · Mathematics 2011-02-21 Luis A. Fernandez , Alexander Y. Khapalov

In this paper, we analyze the null controllability property for a degenerate parabolic equation involving memory terms with a locally distributed control. We first derive a null controllability result for a nonhomogeneous degenerate heat…

Optimization and Control · Mathematics 2021-07-07 Brahim Allal , Genni Fragnelli

It is well known that both the heat equation with Dirichlet or Neumann boundary conditions are null controlable as soon as the control acts in a non trivial domain (i.e. a set of positive measure, see [10, 11, 12, 1, 6]. In this article, we…

Analysis of PDEs · Mathematics 2023-02-14 Iván Moyano , Nicolas Burq

We consider a linear hybrid system composed by two rods of equal length connected by a point mass. We show that the system is null controllable with Dirichlet and Neumann controls. The results are based on a careful spectral spectral…

Optimization and Control · Mathematics 2015-07-29 Scott W. Hansen , Jose de Jesus Martinez

This article is devoted to the analysis of control properties for a heat equation with singular potential $\mu/\delta^2$, defined on a bounded $C^2$ domain $\Omega\subset\mathbb{R}^N$, where $\delta$ is the distance to the boundary…

Analysis of PDEs · Mathematics 2016-02-24 Umberto Biccari , Enrique Zuazua

We derive in a direct and rather straightforward way the null controllability of a 2-D heat equation with boundary control. We use the so-called flatness approach, which consists in parameterizing the solution and the control by the…

Optimization and Control · Mathematics 2013-04-22 Philippe Martin , Lionel Rosier , Pierre Rouchon

This paper studies the approximate and null controllability for impulse controlled systems of heat equations coupled by a pair (A,B) of constant matrices. We present a necessary and sufficient condition for the approximate controllability,…

Optimization and Control · Mathematics 2017-01-23 Shulin Qin , Gengsheng Wang

This paper concerns the null controllability for a class of stochastic degenerate parabolic equations. We first establish a global Carleman estimate for a linear forward stochastic degenerate equation with multiplicative noise. Using this…

Optimization and Control · Mathematics 2022-02-22 M. Baroun , M. Fadili , A. Khchine , L. Maniar

We study null controllability for linear heat-type systems in finite dimensions that incorporate both memory and time-delay effects. A strengthened notion of controllability, referred to as delay and memory-type null controllability, is…

Optimization and Control · Mathematics 2026-01-15 Dev Prakash Jha , Raju K. George

In this paper we consider a linear hybrid system which composed by two non-homogeneous rods connected by a point mass and generated by the equation\bea\left\{ \begin{array}{ll} \rho_{1}(x)u_{t}=(\sigma_{1}(x)u_{x})_{x}-q_{1}(x)u,&…

Optimization and Control · Mathematics 2017-03-09 Jamel Ben Amara , Hedi Bouzidi

We derive in a direct and rather straightforward way the null controllability of the N-dimensional heat equation in a bounded cylinder with boundary control at one end of the cylinder. We use the so-called flatness approach, which consists…

Optimization and Control · Mathematics 2013-10-24 Philippe Martin , Lionel Rosier , Pierre Rouchon

This paper deals with the numerical computation of boundary null controls for the 1D wave equation with a potential. The goal is to compute an approximation of controls that drive the solution from a prescribed initial state to zero at a…

Optimization and Control · Mathematics 2015-02-03 Nicolae Cîndea , Enrique Fernandez-Cara , Arnaud Munch

In this paper, we continue the study of some controllability issues for the forward stochastic parabolic equation with dynamic boundary conditions. The main novelty in the present paper consists of considering only one control without extra…

Analysis of PDEs · Mathematics 2024-03-14 Said Boulite , Abdellatif Elgrou , Lahcen Maniar , Omar Oukdach

In this paper, we consider a linear hybrid system which is composed of $N+1$ non-homogeneous thin rods connected by $N$ interior-point masses with a Dirichlet boundary condition on the left end, and Dirichlet control on the right end. Using…

Analysis of PDEs · Mathematics 2021-09-03 Kaïs Ammari , Hedi Bouzidi

We consider heat operators on a convex domain $\Omega$, with a critically singular potential that diverges as the inverse square of the distance to the boundary of $\Omega$. We establish a general boundary controllability result for such…

Analysis of PDEs · Mathematics 2026-01-28 Alberto Enciso , Arick Shao , Bruno Vergara

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

We consider two degenerate heat equations with a nonlocal space term, studying, in particular, their null controllability property. To this aim, we first consider the associated nonhomogeneous degenerate heat equations: we study their well…

Analysis of PDEs · Mathematics 2023-07-26 B. Allal , G. Fragnelli , J. Salhi

In this paper, we study several theoretical and numerical questions concerning the null controllability problems for linear parabolic equations and systems for several dimensions. The control is distributed and acts on a small subset of the…

Optimization and Control · Mathematics 2024-11-22 Enrique Fernandez-Cara , Roberto Morales , Diego A. Souza

In this study, we study the null controllability of a multi-dimensional degenerate parabolic equation characterized by a degenerate interior point. The control domain, which is an arbitrary inner region, does not encompass the degenerate…

Optimization and Control · Mathematics 2026-05-05 Dong-Hui Yang , Bao-Zhu Guo , Jie Zhong

In this article, we study the null-controllability and observability properties of a bi-dimensio\-nal fluid-structure interaction system, governed by the heat equation coupled with the damped beam equation. To do so, we prove a global…

Analysis of PDEs · Mathematics 2025-06-23 Mehdi Badra , Jérémi Dardé , Emmanuel Zongo