Related papers: Null controllability for stochastic fourth order p…

In this paper, we are concerned with the boundary controllability of heat equation with dynamic boundary conditions. More precisely, we prove that the equation is null controllable at any positive time by means of a boundary control…

The main purpose of this paper is to apply the notion of hierarchical control to a coupled degenerate non linear parabolic equations. We use the Stackelberg-Nash strategy with one leader and two followers. The followers solve a Nash…

This book aims to provide a brief overview of recent advancements in the theory of inverse problems for stochastic partial differential equations. In order to keep the content concise, we will only discuss the inverse problems of two…

We establish new Carleman estimates for the wave equation, which we then apply to derive novel observability inequalities for a general class of linear wave equations. The main features of these inequalities are that (a) they apply to a…

This paper concerns with the hierarchical control of the semilinear parabolic equations with interior degeneracy. By a Stackelberg-Nash strategy, we consider the linear and semilinear system with one leader and two followers. First, for any…

A notion of $L^p$-exact controllability is introduced for linear controlled (forward) stochastic differential equations, for which several sufficient conditions are established. Further, it is proved that the $L^p$-exact controllability,…

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.

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 problem of exact observability is analyzed for a wide class of neutral type systems by an infinite dimensional approach. The duality with the exact controllabil-ity problem is the main tool. It is based on an explicit expression of a…

In this paper we use a Stackelberg-Nash strategy to show the local null controllability of a parabolic equation where the diffusion coefficient is the product of a degenerate function in space and a nonlocal term. We consider one control…

We consider a linear Korteweg-de Vries equation on a bounded domain with a left Dirichlet boundary control.The controllability to the trajectories of such a system was proved in the last decade by using Carleman estimates.Here, we go a step…

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…

In this paper, we are concerned with the null controllability of a linear population dynamics cascade systems (or the so-called prey-predator models) with two different dispersion coefficients which degenerate in the boundary and with one…

In this paper we consider the null controllability for a population model depending on time, on space and on age. Moreover, the diffusion coefficient degenerate at the boundary of the space domain. The novelty of this paper is that for the…

This review examines classical and recent results on controllability and inverse problems for hyperbolic and dispersive equations with dynamic boundary conditions. We aim to illustrate the applicability of Carleman estimates to establish…

This paper extends our previous controllability results for a class of coupled linear parabolic systems with nonlocal interactions, motivated by applications in finance such as generalized Black--Scholes models. We establish local null…

This article presents some controllability and stabilization results for a system of two coupled linear Schr\"odinger equations in the one-dimensional case where the state components are interacting through the Kirchhoff boundary…

This work investigates both local null controllability and large time null controllability for a class of complete Ladyzhenskaya Boussinesq systems, where the controls are distributed and supported on small subsets of the domain. The proof…

In this paper, we investigate the null controllability of nonlinear wave systems. Initially, we employ a combination of the Galerkin method and a fixed point theorem to establish the null controllability for semi-linear wave equations with…

This paper investigates the controllability of finite-dimensional linear fractional systems involving an uncertain parameter. We establish new results on the simultaneous and average controllability. In particular, we show that average…