Related papers: Exact Boundary Controllability for the Boussinesq …
We consider a bilinear control problem for the wave equation on a torus of arbitrary dimension. We show that the system is globally approximately controllable in arbitrarily small times from a dense family of initial states. The control…
Using the semigroup approach to abstract boundary control problems we characterize the space of all exactly reachable states. Moreover, we study the situation when the controls of the system are required to be positive. The abstract results…
We deal with a singularly perturbed optimal control problem with slow and fast variable depending on a parameter {\epsilon}. We study the asymptotic, as {\epsilon} goes to 0, of the corresponding value functions, and show convergence, in…
We consider the 1D linear Schr{\"o}dinger equation, on a bounded interval, with Dirichlet boundary conditions and bilinear scalar control. The small-time local exact controllability around the ground state was proved in [BeaLau10], under an…
In this work, we investigate the small-time global controllability properties of a class of fourth-order nonlinear parabolic equations driven by a bilinear control posed on the one-dimensional torus. The controls depend only on time and act…
In the paper we consider the infinite horizon control problems on the interval with free right-hand endpoint. We obtain the necessary conditions of strict optimality. The method of the proof actually follows the classic paper by Halkin, and…
In this article, we study the local exact controllability to a constant trajectory for a compressible Navier-Stokes-Korteweg system on the torus in dimension $ d\in\{1,2,3\}$ when the control acts on an open subset. To be more precise, we…
This article investigates the exact controllability of three-dimensional stochastic Maxwell equations, a coupled system comprising two stochastic partial differential equations. The research establishes the observability inequality for the…
In this paper we study the boundary controllability for a system of two coupled degenerate/singular parabolic equations with a control acting on only one equation. We analyze both approximate and null boundary controllability properties.…
In this article, we study an initial-boundary-value problem of the sixth order Boussinesq equation on a half line with nonhomogeneous boundary conditions: \[ u_{tt}-u_{xx}+\beta u_{xxxx}-u_{xxxxxx}+(u^2)_{xx}=0,\quad x>0\mbox{, }t>0,\]…
In this paper, we present some controllability results for linear and nonlinear phase-field systems of Caginalp type considered in a bounded interval of $\mathbb R$ when the scalar control force acts on the temperature equation of the…
In this paper we investigate the optimal control problem for a class of stochastic Cauchy evolution problem with non standard boundary dynamic and control. The model is composed by an infinite dimensional dynamical system coupled with a…
In this article we consider a 2-D quantum particle confined a disc whose radius can be deformed continuously in time. We study the problem of controllability of such a quantum particle via deformations of the initial disc, i.e., when we set…
In this work we analyse the small-time reachability properties of a nonlinear parabolic equation, by means of a bilinear control, posed on a torus of arbitrary dimension $d$. Under a saturation hypothesis on the control operators, we show…
We consider optimal control problems governed by systems describing the flow of an incompressible second grade fluid with Dirichlet boundary conditions. We prove the existence of an optimal solution, derive the corresponding necessary…
This paper is devoted to the theoretical and numerical investigation of the initial boundary value problem for a system of equations used for the description of waves in coastal areas, namely, the Boussinesq-Abbott system in the presence of…
This paper studies the controllability problem of a parabolic system of chemotaxis. The local exact controllability to trajectories of the system imposed one control force only is obtained by applying Kakutani's fixed point theorem combined…
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…
We study temperature and velocity output tracking problem for a two-dimensional room model with the fluid dynamics governed by the linearized translated Boussinesq equations. Additionally, the room model includes finite-dimensional models…
We prove global internal controllability in large time for the nonlinear Schrodinger equation on a bounded interval with periodic, Dirichlet or Neumann conditions. Our strategy combines stabilization and local controllability near 0. We use…