相关论文: Null-controllability of non-autonomous Ornstein-Uh…

This work studies the null controllability of a system of coupled parabolic PDEs. In particular, our work specializes to an important subclass of these control problems which are coupled by first and zero-order couplings and are,…

We consider linear systems on a separable Hilbert space $H$, which are null controllable at some time $T_0>0$ under the action of a point or boundary control. Parabolic and hyperbolic control systems usually studied in applications are…

We study the internal non null-controllability properties of the heat equation on 2-dimensional almost-Riemannian manifolds with an interior singularity, and under the assumption that the closure of the control zone does not contain the…

In this paper, we prove the null controllability of some parabolic-elliptic systems. The control is distributed, locally supported in space and appears only in one PDE. The arguments rely on fixed-point reformulation and suitable Carleman…

We consider the control problem for the generalized heat equation for a Schroedinger operator on a domain with a reflection symmetry with respect to a hyperplane. We show that if this system is null-controllable, then so is the system on…

This paper is devoted to the theoretical and numerical analysis of the null controllability of a coupled ODE-heat system internally and at the boundary with Neumann boundary control. First, we establish the null controllability of the…

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…

The global null controllability of stochastic semilinear parabolic equations with globally Lipschitz nonlinearities has been addressed in recent literature. However, there are no results concerning their numerical approximation and the…

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…

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…

We make a complete analysis of the controllability properties from the exterior of the (possible) strong damping wave equation with the fractional Laplace operator subject to the nonhomogeneous Dirichlet type exterior condition. In the…

This paper aims to establish null controllability for systems coupled by two backward fourth order stochastic parabolic equations. The main goal is to control both equations with only one control act on the drift term. To achieve this, we…

We analyze the averaged controllability properties of random evolution Partial Differential Equations. We mainly consider heat and Schr\"odinger equations with random parameters, although the problem is also formulated in an abstract frame.…

In this paper we study boundary controllability of the Korteweg-de Vries (KdV) equation posed on a finite domain $(0,L)$ with the Neumann boundary conditions: u_t+u_x+uu_x+u_{xxx}=0 in (0,L)x(0,T), u_{xx}(0,t)=0, u_x(L,t)=h(t),…

In this paper we focus on the null controllability problem for the heat equation with the so-called inverse square potential and a memory term. To this aim, we first establish the null controllability for a nonhomogeneous singular heat…

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 a separable Hilbert space $X$, we study the controlled evolution equation \begin{equation*} u'(t)+Au(t)+p(t)Bu(t)=0, \end{equation*} where $A\geq-\sigma I$ ($\sigma\geq0$) is a self-adjoint linear operator, $B$ is a bounded linear…

We analyze controllability properties for the one-dimensional heat equation with singular inverse-square potential $$ u_t-u_{xx}-\frac{\mu}{x^2}u=0,\;\;\; (x,t)\in(0,1)\times(0,T).$$ For any $\mu<1/4$, we prove that the equation is null…

Let $\Delta$ be the Dirichlet Laplacian on the interval $(0,\pi)$, and let $T>0$. We prove a well-posedness results for the structurally damped beam equation $$u_{tt}+\Delta^2 u-\rho \Delta u_t=0, x\in (0,\pi),t>0$$ with various boundary…

In this paper, we study the null controllability of forward and backward stochastic semilinear complex Ginzburg-Landau equations with global Lipschitz nonlinear terms. For this purpose, by deriving an improved global Carleman estimates for…