相关论文: Null controllability of a degenerate parabolic equ…

In this work, we prove a Carleman estimate for a parabolic problem which has a dissipative degenerate term. The prove relies on choose a suitable weight function that change of sign inside the control domain.

This review surveys previous and recent results on null controllability and inverse problems for parabolic systems with dynamic boundary conditions. We aim to demonstrate how classical methods such as Carleman estimates can be extended to…

This paper deals with the hierarchic control of a degenerate parabolic equation with missing initial condition. We present a Stackelberg strategy combining the concept of null controllability with low-regret control. We assume that we can…

We establish the null controllability of forward and backward linear stochastic parabolic equations with linear Robin (or Fourier) boundary conditions. These equations incorporate zero and first order terms with bounded coefficients. To…

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,…

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…

We consider a parabolic problem with degeneracy in the interior of the spatial domain and Neumann boundary conditions. In particular, we will focus on the well-posedness of the problem and on Carleman estimates for the associated adjoint…

For $\alpha\in (0,2)$ we study the null controllability of the parabolic operator $$Pu= u_t - (\vert x \vert ^\alpha u_x)_x\qquad (1<x<1),$$ which degenerates at the interior point $x=0$, for locally distributed controls acting only one…

This paper is concerned with the null controllability problem for a class of quasilinear parabolic equations under multiplicative control, locally supported in space. For the purpose of proving the existence of a multiplicative control…

This paper is devoted to studying the null and approximate controllability of two linear coupled parabolic equations posed on a smooth domain of R^N (N>1) with coupling terms of zero and first orders and one control localized in some…

In this work we study the global approximate multiplicative controllability for the linear degenerate parabolic Cauchy-Neumann problem $$ \{{array}{l} \displaystyle{v_t-(a(x) v_x)_x =\alpha (t,x)v\,\,\qquad {in} \qquad Q_T…

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.…

This work is concerned with the possibility of proving the boundary null controllability for the degenerate wave equation, developing the asymptotic analysis of a suitable family of state-control pairs $((u_\varepsilon ,…

In this article we consider a control problem of a linear Euler-Bernoulli damped beam equation with potential in dimension one with periodic boundary conditions. We derive a new Carleman estimate for an adjoint of the equation under…

This paper is devoted to a study of the controllability of a free-boundary problem for a class of one-dimensional degenerate parabolic equations with distributed controls, locally supported in space. We prove that for any $T>0$, if the…

In this paper, we consider the infinite dimensional linear control system describing population models structured by age, size, and spatial position. The diffusion coefficient is degenerate at a point of the domain or both extreme points.…

This article is devoted to the study of null controllability for evolution equations that incorporate both memory and delay effects. The problem is particularly challenging due to the presence of memory integrals and delayed states, which…

We study a control problem governed by a semilinear parabolic equation. The control is a measure that acts as the kernel of a possibly nonlocal time delay term and the functional includes a non-differentiable term with the measure-norm of…

In this paper, we study the null controllability for parabolic SPDEs involving both the state and the gradient of the state. To start with, an improved global Carleman estimate for linear forward (resp. backward) parabolic SPDEs with…

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…