相关论文: Approximate controllability for a 2D Grushin equat…

This analysis is concerned with the controllability of quantum systems in the case where the standard dipolar approximation, involving the permanent dipole moment of the system, is corrected with a polarizability term, involving the field…

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…

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…

In this paper, we consider the well-known Fattorini's criterion for approximate controllability of infinite dimensional linear systems of type $y'=A y+Bu$. We precise the result proved by H. O. Fattorini in \cite{Fattorini1966} for bounded…

We consider two degenerate heat equations with a nonlocal space term, studying, in particular, their null controllability property. To this aim, we first consider the associated nonhomogeneous degenerate heat equations: we study their well…

We present here a constructive method of Lagrangian approximate control- lability for the Euler equation. We emphasize on different options that could be used for numerical recipes: either, in the case of a bi-dimensionnal fluid, the use of…

In the paper, the problems of approximate controllability are studied for the control system $w_t=\Delta w$, $w(0,x_2,t)=u(x_2,t)$, $x_1\in\mathbb R_+=(0,+\infty)$, $x_2\in\mathbb R$, $t\in(0,T)$, where $u$ is a control belonging to a…

This paper is devoted to the study of the approximate controllability for a one-dimensional wave equation in domains with moving boundary. This equation models the motion of a string where an endpoint is fixed and the other one is moving.…

In this paper, we prove the null controllability of a one-dimensional fourth-order degenerate parabolic equation with a singular potential. Here, we analyze cases where boundary control conditions are applied at the left endpoint. We…

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…

The aim of this work is to study the controllability of the bilinear Schr\"odinger equation on compact graphs. In particular, we consider the equation (BSE) $i\partial_t\psi=-\Delta\psi+u(t)B\psi$ in the Hilbert space…

Our goal is to study controllability and observability properties of the 1D heat equation with internal control (or observation) set $\omega_{\varepsilon}=(x_{0}-\varepsilon, x_{0}+\varepsilon )$, in the limit $\varepsilon\rightarrow 0$,…

We derive in a straightforward way the exact controllability of the 1-D Schrodinger equation with a Dirichlet boundary control. We use the so-called flatness approach, which consists in parameterizing the solution and the control by the…

We study the problem of so-called geometric quantum confinement in a class of two-dimensional incomplete Riemannian manifold with metric of Grushin type. We employ a constant-fibre direct integral scheme, in combination with Weyl's analysis…

We consider two dimensional Grushin Schr\"odinger equation posed on a finite cylinder $\Omega=(-1,1)_x\times \T_y$ with Dirichlet boundary condition. We obtain the sharp observability by any horizontal strip, with the optimal time $T_*>0$…

Control properties of the Kawahara equation are considered when the equation is posed on an unbounded domain. Precisely, the paper's main results are related to an approximation theorem that ensures the exact (internal) controllability in…

This result will be published as part of my PhD thesis after some streamlining. This manuscript contains the proof of the claim, but is not peer-reviewed. We prove uniqueness and stability for the inverse problem of the 2D Schr\"odinger…

In this paper, we study several theoretical and numerical questions concerning the null controllability problems for linear parabolic equations and systems for several dimensions. The control is distributed and acts on a small subset of the…

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…

We establish the approximate controllability in $L^2$ for the nonlinear Benjamin-Ono equation on torus via two-dimensional control input. Our proof is based on adaptations of geometric control approach introduced by Agrachev and Sarychev.…