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

We study the observability properties of the Grushin equation with an inverse square potential, whose singularity occurs at the boundary of two-dimensional rectangular domains or in the interior of the domain in higher dimensions. In some…

This paper aims to answer an open problem posed by Morancey in 2015 concerning the null controllability of the heat equation on (-1, 1) with an internal inverse square potential located at x = 0. For the range of singularity under study,…

We study the internal non null-controllability properties of the heat equation on 2-dimensional almost-Riemannian manifolds with an interior singularity, and under the assumption that the closure of the control zone does not contain the…

In this paper, we consider a null controllability and an inverse source problem for stochastic Grushin equation with boundary degeneracy and singularity. We construct two special weight functions to establish two Carleman estimates for the…

We analyze controllability properties for the one-dimensional heat equation with singular inverse-square potential $$ u_t-u_{xx}-\frac{\mu}{x^2}u=0,\;\;\; (x,t)\in(0,1)\times(0,T).$$ For any $\mu<1/4$, we prove that the equation is null…

The approach to Lipschitz stability for uniformly parabolic equations introduced by Imanuvilov and Yamamoto in 1998, based on Carleman estimates, seems hard to apply to the case of Grushin-type operators of interest to this paper. Indeed,…

We investigate the null controllability property of the parabolic equation associated with the Grushin operator defined by the canonical almost-Riemannian structure on the 2-dimensional sphere $\mathbb S^2$. This is the natural…

This paper is devoted to the study of the internal null-controllability of the Grushin equation. We determine the minimal time of controllability for a large class of non-rectangular control region. We establish the positive result thanks…

We consider heat operators on a bounded domain $\Omega \subseteq \mathbb{R}^n$, with a critically singular potential diverging as the inverse square of the distance to $\partial \Omega$. While null boundary controllability for such…

In this paper we focus on the null controllability problem for the heat equation with the so-called inverse square potential and a memory term. To this aim, we first establish the null controllability for a nonhomogeneous singular heat…

This paper explores the controllability of a class of N-dimensional hyperbolic equations featuring a single interior degenerate point. Firstly, we establish the well-posedness of the equation through the application of the Hardy inequality.…

We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder equipped with an incomplete Riemannian metric of Grushin type, in the class of metrics yielding an infinite deficiency…

We explore further controllability problems through a standard least square approach. By setting up a suitable error functional $E$, and putting $m(\ge0)$ for the infimum, we interpret approximate controllability by asking $m=0$, while…

In this paper, we deal with the boundary controllability of a one-dimensional degenerate and singular wave equation with degeneracy and singularity occurring at the boundary of the spatial domain. Exact boundary controllability is proved in…

We study the null controllability of the parabolic equation associated with the Grushin-type operator $A=\partial_x^2+|x|^{2\gamma}\partial_y^2\,, (\gamma>0),$ in the rectangle $\Omega=(-1,1)\times(0,1)$, under an additive control supported…

In this paper, we prove a sharp uniqueness result for the singular Schr\"odinger equation with an inverse square potential. This will be done without assuming geometrical restrictions on the observation region. The proof relies on a recent…

The primary focus of this paper is to establish the internal null controllability for the one-dimensional heat equation featuring dynamic boundary conditions. This achievement is realized by introducing a new Carleman estimate and an…

The goal of this paper is to analyze the pointwise controllability properties of a one-dimensional degenerate/singular equation. We prove the conditions that characterize approximate and null controllability. Besides, a numerical simulation…

This article is devoted to analyze control properties for the heat equation with singular potential $-\mu/|x|^2$ arising at the boundary of a smooth domain $\Omega\subset \rr^N$, $N\geq 1$. This problem was firstly studied by Vancostenoble…

We consider heat operators on a convex domain $\Omega$, with a critically singular potential that diverges as the inverse square of the distance to the boundary of $\Omega$. We establish a general boundary controllability result for such…