Related papers: Stackelberg strategy on a degenerate parabolic equ…

This work is concerned with the obtainment of new Carleman estimates for linear parabolic equations, where the second-order differential operator brings a super strong degeneracy in a positive measure subset of the spatial domain. In order…

The focus of this paper is on the null controllability of two kinds of coupled systems including both degenerate and non-degenerate equations with switching control. We first establish the observability inequality for measurable subsets in…

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 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 paper is concerned with the application of Stackelberg-Nash strategies to control fourth order linear and semi-linear parabolic equations. We assume that the system is acted through a hierarchy of distributed controls: one main control…

In this study, we study the null controllability of a multi-dimensional degenerate parabolic equation characterized by a degenerate interior point. The control domain, which is an arbitrary inner region, does not encompass the degenerate…

In this paper we investigate the Hierarchical null controllability of a coupled degenerate semilinear parabolic equation in domains which are moving in time. We show the local null controllability of the semilinear system using Liusternik's…

We establish the null controllability for linear stochastic fourth order parabolic equations. Utilizing the duality argument, the null controllability is reduced to the observability for backward fourth order stochastic parabolic equations,…

We study the Stackelberg-Nash null controllability of a coupled system governed by two linear forward stochastic parabolic equations. The system includes one leader control localized in a subset of the domain, two additional leader controls…

This paper addresses null controllability for both forward and backward linear stochastic parabolic equations by introducing convection terms on the drift parts with bounded coefficients. Moreover, the forward stochastic parabolic equation…

We study the controllability of a class of $N$-dimensional degenerate parabolic equations with single interior point degeneracy. We employ the Galerkin method to prove the existence of solutions for the equations. The analysis is then…

We prove the null controllability of a cascade system of \(n\) coupled backward stochastic parabolic equations involving both reaction and convection terms, as well as general second-order parabolic operators, with \(n \geq 2\). To achieve…

This paper studies the memory-type null controllability of a class of one-dimensional non-autonomous degenerate parabolic equations with Volterra-type memory terms. The diffusion operator is considered in both divergence and non-divergence…

This paper considers a semi-discrete forward stochastic parabolic operator with homogeneous Dirichlet conditions in arbitrary dimensions. We show the lack of null controllability for a spatial semi-discretization of a null-controllable…

This paper deals with a hierarchical multi-objective control problem for forward stochastic parabolic equations with dynamic boundary conditions. The controls are divided into two classes: leaders and followers. The goal of the leaders is…

This paper studies unique continuation for weakly degenerate parabolic equations in one space dimension. A new Carleman estimate of local type is obtained to deduce that all solutions that vanish on the degeneracy set, together with their…

In this article, we study the uniform null controllability problem for a system of coupled parabolic equations with an oscillating coefficient. This is done in three steps -- first, we study the spectral properties of an elliptic operator;…

We consider a parabolic problem with degeneracy in the interior of the spatial domain, and we focus on controllability results through Carleman estimates for the associated adjoint problem. The novelty of the present paper is that the…

This paper is devoted to studying null controllability for a class of stochastic fourth order semi-discrete parabolic equations, where the spatial variable is discretized with finite difference scheme and the time is kept as a continuous…

The main objective of this paper is to study the hierarchical exact controllability for a parabolic equation with Hardy potential by Stackelberg-Nash strategy. In linear case, we employ Lax-Milgram theorem to prove the existence of an…