Related papers: Variable Support Control for the Wave Equation: A …
The well-known fact following from the Holmgren-John-Tataru uniqueness theorem is a local approximate boundary $L_2$-controllability of the dynamical system governed by the wave equation. Generalizing this result, we establish the…
This paper is concerned with a boundary control problem for the Cahn--Hilliard equation coupled with dynamic boundary conditions. In order to handle the control problem, we restrict our analysis to the case of regular potentials defined on…
We consider the wave equation in a smooth domain subject to Dirichlet boundary conditions on one part of the boundary and dissipative boundary conditions of memory-delay type on the remainder part of the boundary, where a general borelian…
We consider a quantum particle in a 1D interval submitted to a potential. The evolution of this particle is controlled using an external electric field. Taking into account the so-called polarizability term in the model (quadratic with…
In this work we study the controllability and stabilization of the linearized Benjamin equation which models the unidirectional propagation of long waves in a two-fluid system where the lower fluid with greater density is infinitely deep…
We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of…
We investigate the internal controllability of the wave equation with structural damping on the one dimensional torus. We assume that the control is acting on a moving point or on a moving small interval with a constant velocity. We prove…
In this paper, we obtain the exact controllability for a refined stochastic wave equation with three controls by establishing a novel Carleman estimate for a backward hyperbolic-like operator. Compared with the known result, the novelty of…
Approximate controllability of the Euler equations is investigated by means of a finite set of actuators. It is proven that approximate controllability holds if we can find a saturating subset of actuators. The notion of saturating set is…
We prove approximate controllability of the bilinear Schr\"odinger equation in the case in which the uncontrolled Hamiltonian has discrete non-resonant spectrum. The results that are obtained apply both to bounded or unbounded domains and…
Observers are well known in control theory. Originally designed to estimate the hidden states of dynamical systems given some measurements, the observers scope has been recently extended to the estimation of some unknowns, for systems…
In this paper, we consider control constrained $L^2-$Dirichlet boundary control of a convection-diffusion equation on a two dimensional convex polygonal domain. We discretize the control problem based on the local discontinuous Galerkin…
Consider a three-dimensional fluid in a rectangular tank, bounded by a flat bottom, vertical walls and a free surface evolving under the influence of gravity. We prove that one can estimate its energy by looking only at the motion of the…
We study controllability of $d$-dimensional defocusing cubic Schroedinger equation under periodic boundary conditions. The control is applied additively, via a source term, which is a linear combination of few complex exponentials (modes)…
In this paper, motivated by a physics problem, we investigate some numerical and computational aspects for the problem of hierarchical controllability in a one-dimensional wave equation in domains with a moving boundary. Some controls act…
Existing theoretical stabilization results for linear, hyperbolic multi-dimensional problems are extended to the discretized multi-dimensional problems. In contrast to existing theoretical and numerical analysis in the spatially…
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…
We study the problem of controlling the free surface for a two dimensional solid container in the context of the gravity waves and the sloshing problem. By using conformal maps and the Dirichlet-Neumann operator, the problem is formulated…
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…
The paper deals with finite element approximations of elliptic Dirichlet boundary control problems posed on two-dimensional polygonal domains. Error estimates are derived for the approximation of the control and the state variables. Special…