相关论文: Null controllability of an ODE-heat system with co…

The primary focus of this paper is to establish the internal null controllability for the one-dimensional heat equation featuring dynamic boundary conditions. This achievement is realized by introducing a new Carleman estimate and an…

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…

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…

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…

In this paper, we consider the wave equation with both a viscous Kelvin-Voigt and frictional damping as a model of viscoelasticity in which we incorporate an internal control with a moving support. We prove the null controllability when the…

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…

We survey recent results on the control problem for the heat equation on unbounded and large bounded domains. First we formulate new uncertainty relations, respectively spectral inequalities. Then we present an abstract control cost…

In this paper, we recover the boundary null controllability for the degenerate heat equation by analyzing the asymptotic behavior of an eligible family of state-control pairs $((u_{\varepsilon}, h_{\varepsilon}))_{\varepsilon >0}$ solving…

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,&…

We make two remarks about the null-controllability of the heat equation with Dirichlet condition in unbounded domains. Firstly, we give a geometric necessary condition (for interior null-controllability in the Euclidean setting)which…

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,…

We prove null controllability for linear and semilinear heat equations with dynamic boundary conditions of surface diffusion type. The results are based on a new Carleman estimate for this type of boundary conditions.

We consider a linear nonlocal heat equation in a bounded domain $\Omega\subset\mathbb{R}^d$ with Dirichlet boundary conditions. The non-locality is given by the presence of an integral kernel. We analyze the problem of controllability when…

The focus of this paper is on the null controllability of two kinds of coupled systems including both degenerate and non-degenerate equations with switching control. We first establish the observability inequality for measurable subsets in…

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…

In this paper, we consider a nonlinear system of two parabolic equations, with a distributed control in the first equation and an odd coupling term in the second one. We prove that the nonlinear system is small-time locally…

We consider the control problem of the heat equation on bounded and unbounded domains, and more generally the corresponding inhomogeneous equation for the Schr\"odinger semigroup. We show that if the sequence of null-controls associated to…

We derive in a straightforward way the null controllability of a 1-D heat equation with boundary control. We use the so-called {\em flatness approach}, which consists in parameterizing the solution and the control by the derivatives of a…

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…

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…