Related papers: Coupled linear Schr\"odinger equations: Control an…
In this paper, we study the null controllability of weakly degenerate coupled parabolic systems with two different diffusion coefficients and one control force. To obtain this aim, we develop first new global Carleman estimates for…
In this paper, we present a new Carleman estimate for the adjoint equations associated to a class of super strong degenerate parabolic linear problems. Our approach considers a standard geometric imposition on the control domain, which can…
The goal of this work is to prove global controllability and stabilization properties for the fractional Schr\"odinger equation on $d$-dimensional compact Riemannian manifolds without boundary $(M,g)$. To prove our main results we use…
We consider a linear Schr\"odinger equation, on a bounded domain, with bilinear control, representing a quantum particle in an electric field (the control). Recently, Nersesyan proposed explicit feedback laws and proved the existence of a…
In this paper, we intend to present some already known results about the internal controllability of the linear and nonlinear Schr\"odinger equation. After presenting the basic properties of the equation, we give a self contained proof of…
This note presents a sufficient condition for partial approximate ensemble controllability of a set of bilinear conservative quantum systems in an infinite dimensional Hilbert space. The proof relies on classical geometric and averaging…
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),…
We present a sufficient condition for approximate controllability of the bilinear discrete-spectrum Schr\"odinger equation exploiting the use of several controls. The controllability result extends to simultaneous controllability,…
In this article we study the local controllability of the one-dimensional Cahn-Hilliard-Navier-Stokes equation, that is Cahn-Hilliard-Burgers' equation, around a certain steady state using a localized interior control acting only in the…
We consider a class of nonlinear Schr\"odinger equation in two space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in $L^2$)…
We propose a model using the Korteweg-de Vries $(KdV)$ equation on a finite star-shaped network. We first prove the well-posedness of the system and give some regularity results. Then we prove that the energy of the solutions of the…
This paper deals with the exact controllability to the trajectories of the one--phase Stefan problem in one spatial dimension. This is a free-boundary problem that models solidification and melting processes. It is assumed that the physical…
This paper is devoted to the study of the null and approximate controllability for some classes of linear coupled parabolic systems with less controls than equations. More precisely, for a given bounded domain in R^N, we consider a system…
We are concerned about the null controllability of a linear degenerate parabolic equation with one delay parameter on the line $(0,1)$, where the control force is exerted on a subdomain of $(0,1)$ or on the boundary. For that we show how…
This paper concerns the null controllability for a class of stochastic degenerate parabolic equations. We first establish a global Carleman estimate for a linear forward stochastic degenerate equation with multiplicative noise. Using this…
In this paper we present a null controllability result for a degenerate semilinear parabolic equation with first order terms. The main result is obtained after the proof of a new Carleman inequality for a degenerate linear parabolic…
In this paper we use a Stackelberg-Nash strategy to show the local null controllability of a semilinear parabolic equation in one-dimension defined in a non-cylindrical domain where the diffusion coefficient degenerates at one point 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)…
We study the controllability of a linear KdV-Schr{\"o}dinger equation on the one-dimensional torus via purely imaginary bilinear controls. Considering controls spanning a suitable finite number of Fourier modes, we prove small-time global…
In this paper, we establish a boundary observability estimate for stochastic Schr\"{o}dinger equations by means of the global Carleman estimate. Our Carleman estimate is based on a new fundamental identity for a stochastic…