Related papers: Controllability of evolution equations with memory
In this paper, we present a null controllability result for a class of stochastic semi-discrete parabolic equations. For this purpose, an observability estimate is established for backward stochastic semi-discrete parabolic equations, with…
We deal with a degenerate model describing the dynamics of a population depending on time, on age and on space. We assume that the degeneracy can occur at the boundary or in the interior of the space domain and we focus on null…
In this paper we consider the heat equation with memory in a bounded region $\Omega \subset\mathbb{R}^d$, $d\geq 1$, in the case that the propagation speed of the signal is infinite (i.e. the Colemann-Gurtin model). The memory kernel is of…
We prove a Carleman estimate for a one-dimensional parabolic equation which degenerates at one extremity of the domain and has a bounded, time dependent coefficient multiplying the diffusion term. Then we use the estimate to show the null…
In this paper, we are concerned with the null controllability of a linear population dynamics cascade systems (or the so-called prey-predator models) with two different dispersion coefficients which degenerate in the boundary and with one…
The paper deals with exact null-controllability problem for a linear control system consisting of two serially connected abstract control systems. Controllability conditions are obtained. Applications to the exact null-controllability for…
In this paper we will generalize the Kalman rank condition for the null controllability to $n$-coupled linear degenerate parabolic systems with constant coefficients, diagonalizable diffusion matrix, and $m$-controls. For that we prove a…
In this paper, we consider a class of second-order evolution differential inclusions in Hilbert spaces. This paper deals with the approximate controllability for a class of second-order control systems. First, we establish a set of…
We establish the null controllability of forward and backward linear stochastic parabolic equations with linear Robin (or Fourier) boundary conditions. These equations incorporate zero and first order terms with bounded coefficients. To…
We consider a system of two parabolic equations with a forcing term present in one equation and a cubic coupling term in the other one. We prove that the system is locally null controllable.
The problem of exact observability is analyzed for a wide class of neutral type systems by an infinite dimensional approach. The duality with the exact controllabil-ity problem is the main tool. It is based on an explicit expression of a…
In this article we establish the well-posedness, energy estimates, stability, and local null controllability for the thermistor system modeled by a parabolic-parabolic system using a control force acting on just one equation of the system.…
In this article, we consider the infinite dimensional linear control system describing the Population Models Structured by Age, Size, and Spatial Position. The control is localized in the space variable as well as with respect to the age…
We study two notions of controllability on a parabolic system with coupling terms of order one. Based on existing results on, on one side parabolic systems with coupling terms of order zero, and on the other one parabolic systems with…
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…
In this paper, we continue the study of some controllability issues for the forward stochastic heat equation with dynamic boundary conditions. The main novelty in the present paper consists of considering only one control without extra…
A study of the linear quadratic (LQ) control problem on a finite time interval for a model equation in Hilbert spaces which comprehends the memory of the inputs was performed recently by the authors. The outcome included a closed-loop…
In this paper, we study the null controllability of weakly degenerate coupled parabolic systems with two different diffusion coefficients and one control force. To obtain this aim, we develop first new global Carleman estimates for…
This paper explores the controllability of a class of N-dimensional hyperbolic equations featuring a single interior degenerate point. Firstly, we establish the well-posedness of the equation through the application of the Hardy inequality.…
This paper is concerned with impulse approximate controllability for stochastic evolution equations with impulse controls. As direct applications, we formulate captivating minimal norm and time optimal control problems; The minimal norm…