Related papers: The uniform controllability property of semidiscre…
The global null controllability of stochastic semilinear parabolic equations with globally Lipschitz nonlinearities has been addressed in recent literature. However, there are no results concerning their numerical approximation and the…
This manuscript is concerned with the approximate controllability of fractional nonlinear differential equations with nonlocal conditions of order $1<q<2$ in Banach spaces. As far as we know, few articles have investigated this issue. The…
In this work, we investigate the $L^p$- partial null controllability of the abstract semilinear fractional-order differential inclusion with nonlocal conditions. The set of admissible controls is characterized by $u\in L^p(I,U)$,…
The objective of the paper is to investigate the approximate controllability property of a linear stochastic control system with values in a separable real Hilbert space. In a first step we prove the existence and uniqueness for the…
In this article we study a controllability problem for a parabolic and a hyperbolic partial differential equations in which the control is the shape of the domain where the equation holds. The quantity to be controlled is the trace of the…
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…
Based on an algebraic point of view and the realization theory developed by Y. Yamamoto, the present paper states a necessary and sufficient criterion, given in the frequency domain, for the $L^q$ approximate controllability in finite time…
In the paper, the problems of approximate controllability are studied for the control system $w_t=\Delta w$, $w(0,x_2,t)=u(x_2,t)$, $x_1\in\mathbb R_+=(0,+\infty)$, $x_2\in\mathbb R$, $t\in(0,T)$, where $u$ is a control belonging to a…
This paper is devoted to the study of the null and approximate controllability for some classes of linear coupled parabolic systems with less controls than equations. More precisely, for a given bounded domain in R^N, we consider a system…
We study the performance of the certainty equivalent controller on Linear Quadratic (LQ) control problems with unknown transition dynamics. We show that for both the fully and partially observed settings, the sub-optimality gap between the…
In this paper we are concerned with the approximate controllability of a multidimensional semilinear reaction-diffusion equation governed by a multiplicative control, which is locally distributed in the reaction term. For a given initial…
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 consider a semi-linear heat equation with Dirichlet boundary conditions and globally Lipschitz nonlinearity, posed on a bounded domain of R^N (N $\in$ N *), assumed to be an unknown perturbation of a reference domain. We are interested…
In many practical applications of control theory some constraints on the state and/or on the control need to be imposed. In this paper, we prove controllability results for semilinear parabolic equations under positivity constraints on the…
In this paper, a quadratic optimal control problem is considered for second-order parabolic PDEs with homogeneous Dirichlet boundary conditions, in which the "point" control function (depending only on time) constitutes a source term. These…
We study abstract sufficient criteria for open-loop stabilizability of linear control systems in a Banach space with a bounded control operator, which build up and generalize a sufficient condition for null-controllability in Banach spaces…
In this paper, we study the global approximate multiplicative controllability for nonlinear degenerate parabolic Cauchy-Neumann problems. First, we will obtain embedding results for weighted Sobolev spaces, that have proved decisive in…
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) =…
We study several controllability properties for some semilinear parabolic PDE with a quadratic gradient term. For internal distributed controls, it is shown that the system is approximately and null controllable. The proof relies on the…
The aim of this paper is to extend the global error estimation and control addressed in Lang and Verwer [SIAM J. Sci. Comput. 29, 2007] for initial value problems to finite difference solutions of semilinear parabolic partial differential…