Related papers: Boundary controllability for a one-dimensional hea…
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…
We investigate approximate null-controllability for semi-discrete heat equations on the lattice $h\mathbb{Z}^d$ with a potential. By establishing spectral inequalities for the discrete Schr{\"o}dinger operator $P_h = -\Delta_h + V$ on…
This paper deals with the insensitizing controllability property of the quasilinear parabolic equation with dynamic boundary conditions. This problem can be reformulated as a null controllability problem for a cascade quasilinear system…
In this paper we consider the one-phase Stefan problem with surface tension, set in a two-dimensional strip-like geometry, with periodic boundary conditions respect to the horizontal direction $x_1\in\mathbb{T}$. We prove that the system is…
This paper focuses on boundary approximate controllability under positivity constraints of a wide range of infinite-dimensional control systems. We develop frequency domain controllability criteria. Firstly, we derive a controllability…
This paper concerns a controllability problem for blowup points on heat equation. It can be described as follows: In the absence of control, the solution to the linear heat system globally exists in a bounded domain $\Omega$. While, for a…
In this article, we investigate null controllability of the Kuramoto-Sivashinsky (KS) equation on a cylindrical domain $\Omega=\Omega_x\times \Omega_y$ in $\mathbb R^N$, where $\Omega_x=(0,a),$ $a>0$ and $\Omega_y$ is a smooth domain in…
In this paper we study the boundary controllability of the Gear-Grimshaw system posed on a finite domain $(0,L)$, with Neumann boundary conditions: \begin{equation} \label{abs} \begin{cases} u_t + uu_x+u_{xxx} + a v_{xxx} + a_1vv_x+a_2…
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 use moment-SOS (Sum Of Squares) relaxations to address the optimal control problem of the 1D heat equation perturbed with a nonlinear term. We extend the current framework of moment-based optimal control of PDEs to consider a quadratic…
In this article, we study boundary null controllability properties of the linearized compressible Navier-Stokes equations in the interval $(0,2\pi)$ for both barotropic and non-barotropic fluids using only one boundary control. We consider…
We consider an infinite strip $\Omega_L=(0,2\pi L)^{d-1}\times\mathbb{R}$, $d\geq 2$, $L>0$, and study the control problem of the heat equation on $\Omega_L$ with Dirichlet or Neumann boundary conditions, and control set…
In this work, we establish a Carleman inequality for the heat equation with Fourier boundary conditions of the form $\partial_\nu y+by=f1_\gamma$, where the control acts on a small portion $\gamma$ of the boundary. We apply this inequality…
For $\alpha\in (0,2)$ we study the null controllability of the parabolic operator $$Pu= u_t - (\vert x \vert ^\alpha u_x)_x\qquad (1<x<1),$$ which degenerates at the interior point $x=0$, for locally distributed controls acting only one…
We study the null-controllability properties of a one-dimensional wave equation with memory associated with the fractional Laplace operator. The goal is not only to drive the displacement and the velocity to rest at some time-instant but…
We derive in a direct way the exact controllability of the 1D free Schr\"odinger equation with Dirichlet boundary control. We use the so-called flatness approach, which consists in parametrizing the solution and the control by the…
We prove that the approximate null-controllability with uniform cost of the hypoelliptic Ornstein-Uhlenbeck equations posed on $\mathbb R^n$ is characterized by an integral thickness geometric condition on the control supports. We also…
In many practical applications of control theory some constraints on the state and/or on the control need to be imposed. In this paper, we prove controllability results for semilinear parabolic equations under positivity constraints on the…
We study the observability properties of the Grushin equation with an inverse square potential, whose singularity occurs at the boundary of two-dimensional rectangular domains or in the interior of the domain in higher dimensions. In some…
In this paper, we deal with the boundary controllability and boundary stabilizability of the 1D wave equation in non-cylindrical domain of the form ($\alpha (t)<x<\beta (t)$). By using the characteristics method, we prove under a natural…