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In this paper, we study some controllability and observability problems for stochastic systems coupling fourth- and second-order parabolic equations. The main goal is to control both equations with only one controller localized on the drift…

We consider two degenerate heat equations with a nonlocal space term, studying, in particular, their null controllability property. To this aim, we first consider the associated nonhomogeneous degenerate heat equations: we study their well…

In this paper, we recover the boundary null controllability for the degenerate heat equation by analyzing the asymptotic behavior of an eligible family of state-control pairs $((u_{\varepsilon}, h_{\varepsilon}))_{\varepsilon >0}$ solving…

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…

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 study the null controllability for a stochastic semilinear CahnHilliard type equation, whose semilinear term contains first and second order derivatives of solutions. To start with, an improved global Carleman estimate for…

We consider an optimal control problem of diffusion equation with missing data governed by the fractional Laplacian with homogeneous Dirichlet boundary conditions on an arbitrary interaction domain disjoint from the domain of the state…

We consider a $2\times 2$ system of parabolic equations with first and zeroth coupling and establish a Carleman estimate by extra data of only one component without data of initial values. Then we apply the Carleman estimate to inverse…

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.…

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 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 this paper, we consider a hierarchical control problem with model uncertainty. Specifically, we consider the following objectives that we would like to accomplish. The first one being of a controllability-type that consists of…

This article is devoted to studying the null controllability of evolution equations with memory terms. The problem is challenging not only because the state equation contains memory terms but also because the classical controllability…

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…

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…

We show Carleman estimates, observability inequalities and null controllability results for parabolic equations with non smooth coefficients degenerating at an interior point.

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…

This work serves as a continuation of our preceding paper [28]. In that study, we presented a separable variable method to derive the Lebeau-Robbiano spectral inequality for a specific degenerate parabolic equation and subsequently employed…

We study the null controllability for a degenerate/singular wave equation with drift in non divergence form. In particular, considering a control localized on the non degenerate boundary point, we provide some conditions for the boundary…

In this paper, we investigate an optimal control problem governed by parabolic equations with measure-valued controls over time. We establish the well-posedness of the optimal control problem and derive the first-order optimality condition…