Related papers: A hyperbolic system and the cost of null controlla…
In this work, we investigate the optimal cost of null controllability for the $n$-dimensional Stokes system when the control acts on $n-1$ scalar components. We establish a novel spectral estimate for low frequencies of the Stokes operator,…
In this paper, we study the stabilization problem for a hyperbolic type Stokes system posed on a bounded domain. We show that when the damping effects are restricted to a subdomain satisfying the geometrical control condition the system…
In this paper, we discuss our recent works on the null-controllability, the exact controllability, and the stabilization of linear hyperbolic systems in one dimensional space using boundary controls on one side for the optimal time. Under…
This paper considers the controllability of a class of coupled Stokes systems with distributed controls. The coupling terms are of a different nature. The first coupling is through the principal part of the Stokes operator with a constant…
Over the past two decades, the controllability of several examples of parabolic-hyperbolic systems has been investigated. The present article is the beginning of an attempt to find a unified framework that encompasses and generalizes the…
In this paper, we study the null controllability of the three-dimensional Stokes equations with a memory term. For any positive final time $T>0$, we construct initial conditions such that the null controllability does not hold even if the…
The optimal time for the controllability of linear hyperbolic systems in one dimensional space with one-side controls has been obtained recently for time-independent coefficients in our previous works. In this paper, we consider linear…
The goal of this article is to present the minimal time needed for the null controllability and finite-time stabilization of one-dimensional first-order $2 \times 2$ linear hyperbolic systems. The main technical point is to show that we…
This paper is devoted to the controllability of a general linear hyperbolic system in one space dimension using boundary controls on one side. Under precise and generic assumptions on the boundary conditions on the other side, we previously…
In this paper, the null controllability in any positive time T of the first-order equation (1) x'(t)=e^{i\theta}Ax(t)+Bu(t) (|\theta|<\pi/2 fixed) is deduced from the null controllability in some positive time L of the second-order equation…
This paper investigates the exact controllability problem for multi-dimensional stochastic first-order symmetric hyperbolic systems with control inputs acting in two distinct ways: an internal control applied to the diffusion term and a…
This article concerns the exact controllability of unitary groups on Hilbert spaces with unbounded control operator. It provides a necessary and sufficient condition not involving time which blends a resolvent estimate and an observability…
In this paper, we consider the cost of null controllability for a large class of linear equations of parabolic or dispersive type in one space dimension in small time. By extending the work of Tenenbaum and Tucsnak in "New blow-up rates for…
In this work we present new results on the cost of the boundary controllability of parabolic systems at time $T > 0$. In particular, we will study optimal estimates of the control cost at time $T$ ($T$ small enough) when the eigenvalues of…
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…
We are concerned about the controllability of a general linear hyperbolic system of the form $\partial_t w (t, x) = \Sigma(x) \partial_x w (t, x) + \gamma C(x) w(t, x) $ ($\gamma \in \mR$) in one space dimension using boundary controls on…
We prove the null controllability of a cascade system of \(n\) coupled backward stochastic parabolic equations involving both reaction and convection terms, as well as general second-order parabolic operators, with \(n \geq 2\). To achieve…
This paper addresses the controllability of a class of quasi-linear parabolic equations governed by multiplicative controls with mobile support. To prove the existence of such a control forcing the solution to rest at time $T>0$, we first…
In the paper, problems of controllability, approximate controllability, reachability and approximate reachability are studied for the control system $w_t=w_{xx}$, $w(0,\cdot)=u$, $x>0$, $t\in(0,T)$, where $u\in L^\infty(0,T)$ is a control.…
In this paper, we consider forward stochastic nonlinear parabolic equations, with a control localized in the drift term. Under suitable assumptions, we prove the small-time global null-controllability, with a truncated nonlinearity. We also…