Related papers: Hierarchic control for the coupled fourth order pa…

This paper is devoted to studying the null and approximate controllability of two linear coupled parabolic equations posed on a smooth domain of R^N (N>1) with coupling terms of zero and first orders and one control localized in some…

In this paper we present a null controllability result for a degenerate semilinear parabolic equation with first order terms. The main result is obtained after the proof of a new Carleman inequality for a degenerate linear parabolic…

In this article, we study the uniform null controllability problem for a system of coupled parabolic equations with an oscillating coefficient. This is done in three steps -- first, we study the spectral properties of an elliptic operator;…

In this paper, we consider a fourth order inner-controlled parabolic equation on an open bounded subset of $R^d$, or a smooth compact manifold with boundary, along with general boundary operators fulfilling the Lopatinskii-Sapiro condition.…

This paper concerns the null controllability for a class of stochastic degenerate parabolic equations. We first establish a global Carleman estimate for a linear forward stochastic degenerate equation with multiplicative noise. Using this…

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…

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…

This paper addresses null controllability for both forward and backward linear stochastic parabolic equations by introducing convection terms on the drift parts with bounded coefficients. Moreover, the forward stochastic parabolic equation…

In this paper, we study several theoretical and numerical questions concerning the null controllability problems for linear parabolic equations and systems for several dimensions. The control is distributed and acts on a small subset of the…

We prove a Carleman estimate for a one-dimensional parabolic equation which degenerates at one extremity of the domain and has a bounded, time dependent coefficient multiplying the diffusion term. Then we use the estimate to show the null…

We consider a system of two parabolic equations with a forcing term present in one equation and a cubic coupling term in the other one. We prove that the system is locally null controllable.

This work investigates the existence and uniqueness of the Nash equilibrium (solutions to competitive problems in which individual controls aim at separate desired states) for a bi-objective optimal control problem governed by a fractional…

In this study, we employ the established Carleman estimates and propagation estimates of smallness from measurable sets for real analytic functions, along with the telescoping series method, to establish an observability inequality for the…

This paper is devoted to the controllability of linear systems of two coupled parabolic equations when the coupling involves a space dependent first order term. This system is set on an bounded interval, and the first equation is controlled…

In this paper, we present a new Carleman estimate for the adjoint equations associated to a class of super strong degenerate parabolic linear problems. Our approach considers a standard geometric imposition on the control domain, which can…

In this paper, we continue the study of some controllability issues for the forward stochastic parabolic equation with dynamic boundary conditions. The main novelty in the present paper consists of considering only one control without extra…

In this article we study the local controllability of the one-dimensional Cahn-Hilliard-Navier-Stokes equation, that is Cahn-Hilliard-Burgers' equation, around a certain steady state using a localized interior control acting only in the…

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…

In this paper, we prove the small-time global null-controllability of forward (resp. backward) semilinear stochastic parabolic equations with globally Lipschitz nonlinearities in the drift and diffusion terms (resp. in the drift term). In…

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.…