Related papers: Approximate controllability for a 2D Grushin equat…
In this paper, we establish two Carleman estimates for a stochastic degenerate parabolic equation. The first one is for the backward stochastic degenerate parabolic equation with singular weight function. Combining this Carleman estimate…
We prove the null controllability of a one-dimensional degenerate parabolic equation with drift and a singular potential. Here, we consider a weighted Neumann boundary control at the left endpoint, where the potential arises. We use a…
In this paper, the discontinuous Petrov--Galerkin approximation of the Laplace eigenvalue problem is discussed. We consider in particular the primal and ultra weak formulations of the problem and prove the convergence together with a priori…
The paper deals with controllability problem for a distributed system governed by the two-dimensional Gurtin-Pipkin equation. We consider a system with compactly supported distributed control and show that if the memory kernel is a twice…
This work investigates both local null controllability and large time null controllability for a class of complete Ladyzhenskaya Boussinesq systems, where the controls are distributed and supported on small subsets of the domain. The proof…
We are interested in the determination of the reachable states for the boundary control of the one-dimensional heat equation. We consider either one or two boundary controls. We show that reachable states associated with square integrable…
With the advent of quantum technologies, control issues are becoming increasingly important. In this article, we address the control in phase space under a global constraint provided by a minimal energy-like cost function and a local (in…
In this paper we study exact boundary controllability for a linear wave equation with strong and weak interior degeneration of the coefficient in the principle part of the elliptic operator. The objective is to provide a well-posedness…
In this paper we establish a Lebeau-Robbiano spectral inequality for a degenerate one dimensional elliptic operator. Carleman techniques and moment method are combined. Application to null controllability on a measurable set in time for the…
We study the controllability of a Partial Differential Equation of transport type, that arises in crowd models. We are interested in controlling it with a control being a vector field, representing a perturbation of the velocity, localized…
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 time-pointwise quantitative unique continuation estimates for the evolution operators associated to (fractional powers of) the Baouendi--Grushin operators on the cylinder $\mathbb{R}^d \times \mathbb{T}^d$. Corresponding spectral…
This article deals with the boundary null controllability of some degenerate parabolic equations posed on a square domain, presenting the first study of boundary controllability for such equations in multidimensional settings. The proof…
This project investigates the approximate controllability of a class of stochastic integrodifferential equations in Hilbert space with non-local beginning conditions. In a departure from the conventional concerns expressed in the…
The article considers a two-level open quantum system, whose evolution is governed by the Gorini--Kossakowski--Lindblad--Sudarshan master equation with Hamiltonian and dissipation superoperator depending, correspondingly, on piecewise…
This paper deals with the numerical computation of boundary null controls for the 1D wave equation with a potential. The goal is to compute an approximation of controls that drive the solution from a prescribed initial state to zero at a…
This paper is addressed to studying the exact controllability for stochastic Schr\"{o}dinger equations by two controls. One is a boundary control in the drift term and the other is an internal control in the diffusion term. By means of the…
This paper uses the resolvent operator technique to investigate second-order non-autonomous neutral integrodifferential equations with impulsive conditions in a Banach space. We study the existence of a mild solution and the system's…
We consider a system of an arbitrary number of \textsc{1d} linear Schr\"odinger equations on a bounded interval with bilinear control. We prove global exact controllability in large time of these $N$ equations with a single control. This…
This paper is addressed to studying the exact controllability for stochastic transport equations by two controls: one is a boundary control imposed on the drift term and the other is an internal control imposed on the diffusion term. By…