Related papers: Partial null controllability of parabolic linear s…
We consider systems of parabolic equations coupled in zero order terms in a star-like or a tree-like shape, with an internal control acting in only one of the equations. We obtain local exact controllability to the stationary solutions of…
We study (approximate) null-controllability of parabolic equations in $L_p(\mathbb{R}^d)$ and provide explicit bounds on the control cost. In particular we consider systems of the form $\dot{x}(t) = -A_p x(t) + \mathbf{1}_E u(t)$, $x(0) =…
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…
The distributed null controllability for coupled parabolic systems with non-diagonalizable diffusion matrices with a reduced number of controls has been studied in the case of constant matrices. On the other hand, boundary controllability…
Over the past two decades, the controllability of several examples of parabolic-hyperbolic systems has been investigated. The present article is the beginning of an attempt to find a unified framework that encompasses and generalizes the…
This paper proposes an optimal control problem for a parabolic equation with a nonlocal nonlinearity. The system is described by a parabolic equation involving a nonlinear term that depends on the solution and its integral over the domain.…
The goal of the present article is to study controllability properties of mixed systems of linear parabolic-transport equations, with possibly non-diagonalizable diffusion matrix, on the one-dimensional torus. The equations are coupled by…
This paper is addressed to a study of the null controllability for the semilinear parabolic equation with a complex principal part. For this purpose, we establish a key weighted identity for partial differential operators…
For linear infinite systems the approximate controllability problem by control constraints is considered. Controllability conditions represented via system parameters are obtained. Partial differential control systems and control systems…
We study the controllability of a coupled system of linear parabolic equations, with non-negativity constraint on the state. We establish two results of controllability to trajectories in large time: one for diagonal diffusion matrices with…
In this paper, we are concerned with the controllability of a chemotaxis system of parabolic-elliptic type. By linearizing the nonlinear system into two separated linear equations to bypass the obstacle caused by the nonlinear drift term,…
The paper puts forward sufficient conditions for local controllability of a control dynamical system. The results obtained are meaningful in the case when the linear approximation to this system is not completely controllable. As a…
This paper is concerned with the existence of insensitizing controls for a fourth order semilinear parabolic equation. Here, the initial data is partially unknown, we would like to find controls such that a specific functional is…
We prove the interior null-controllability of one-dimensional parabolic equations with time independent measurable coefficients.
In this paper we study the null controllability of some non diagonalizable degenerate parabolic systems of PDEs, we assume that the diffusion, coupling and controls matrices are constant and we characterize the null controllability by an…
In this paper we study the local boundary controllability for a non linear system of two degenerate parabolic equations with a control acting on only one equation. We analyze boundary null controllability properties for the linear system…
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…
In \cite{LPP:2025}, it was shown that, in arbitrary dimension, the spatial semi-discretization of a controlled stochastic parabolic operator is generically not null-controllable. Nevertheless, $\phi$-null controllability results remain…
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…
We study two notions of controllability on a parabolic system with coupling terms of order one. Based on existing results on, on one side parabolic systems with coupling terms of order zero, and on the other one parabolic systems with…