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We obtain sharp convergence rates, using Dirichlet correctors, for solutions of wave equations in a bounded domain with rapidly oscillating periodic coefficients. The results are used to prove the exact boundary controllability that is…
In this paper, we continue the study of some controllability issues for the forward stochastic heat equation with dynamic boundary conditions. The main novelty in the present paper consists of considering only one control without extra…
In this paper, we study the controllability of a Schr\"odinger equation with mixed boundary conditions on disjoint subsets of the boundary: dynamic boundary condition of Wentzell type, and Dirichlet boundary condition. The main result of…
This paper studies optimal control and stabilization problems for continuous-time mean-field systems with input delay, which are the fundamental development of control and stabilization problems for mean-field systems. There are two main…
The semilinear heat equation with non-instantaneous impulses \textbf{(NII)}, memory, and delay is considered and its approximate controllability is obtained. This is done by employing a technique that avoids fixed point theorems and pulls…
We consider a one-dimensional controlled reaction-diffusion equation, where the control acts on the boundary and is subject to a constant delay. Such a model is a paradigm for more general parabolic systems coupled with a transport…
We study the problems of controllability and ergodicity of the system of 3D primitive equations modeling large-scale oceanic and atmospheric motions. The system is driven by an additive force acting only on a finite number of Fourier modes…
This work presents a theoretical framework for the safety-critical control of time delay systems. The theory of control barrier functions, that provides formal safety guarantees for delay-free systems, is extended to systems with state…
We consider a control problem where the system is driven by a decoupled as well as a coupled forward-backward stochastic differential equation. We prove the existence of an optimal control in the class of relaxed controls, which are…
We consider the 1D nonlinear Schr\"odinger equation with bilinear control. In the case of Neumann boundary conditions, local exact controllability of this equation near the ground state has been proved by Beauchard and Laurent in…
In this paper we establish an observability inequality for the heat equation with bounded potentials on the whole space. Roughly speaking, such a kind of inequality says that the total energy of solutions can be controlled by the energy…
We study a general class of control systems with memory, which in particular includes systems with fractional derivatives and integrals and also the standard heat equation. We prove that the approximate controllability property of the heat…
We consider a linear nonlocal heat equation in a bounded domain $\Omega\subset\mathbb{R}^d$ with Dirichlet boundary conditions. The non-locality is given by the presence of an integral kernel. We analyze the problem of controllability when…
This article is devoted to study the interior approximated controllability of the strongly damped semilinear wave equation with memory, impulses and delay terms. The problem is challenging since the state equation contains memory and…
In this paper, we obtain the exact controllability for a refined stochastic wave equation with three controls by establishing a novel Carleman estimate for a backward hyperbolic-like operator. Compared with the known result, the novelty of…
We will consider exact controllability of the distributed system governed by the wave equation with memory. It will be proved that this mechanical system can be driven to rest in finite time, the absolute value of the distributed control…
We analyze the control properties of heat equations with memory terms. We recall previous results showing that if the moving support of the control covers the whole domain where heat diffuses, the system is null controllable when the memory…
Some recent works have shown that the heat equation posed on the whole Euclidean space is null-controllable in any positive time if and only if the control subset is a thick set. This necessary and sufficient condition for…
The paper deals with the controllability of a degenerate beam equation. In particular, we assume that the left end of the beam is fixed, while a suitable control $f$ acts on the right end of it. As a first step we prove the existence of a…
In this paper, we are concerned with local controllability properties of degenerate parabolic equations in bounded domains that evolve in time. More precisely, we deal with the exact controllability to a positive trajectory of a…