Related papers: Null Controllability for Backward Stochastic Parab…
We prove the null controllability of a one dimensional degenerate parabolic equation with drift and a singular potential. We study the case the potential arises at the left end point and the weighted Dirichlet boundary control is located at…
We consider heat operators on a convex domain $\Omega$, with a critically singular potential that diverges as the inverse square of the distance to the boundary of $\Omega$. We establish a general boundary controllability result for such…
In this work, we investigate the approximate controllability of a class of one-dimensional degenerate parabolic equations with Robin boundary conditions. The degeneracy occurs at one endpoint of the spatial domain, and we apply an impulsive…
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 derive a boundary and an internal observability inequality for stochastic hyperbolic equations with nonsmooth lower order terms. The required inequalities are obtained by global Carleman estimate for stochastic hyperbolic…
In this paper, we prove the null controllability of some parabolic-elliptic systems. The control is distributed, locally supported in space and appears only in one PDE. The arguments rely on fixed-point reformulation and suitable Carleman…
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…
The aim of this paper is to perform a Stackelberg strategy to control parabolic equations. We have one control, \textit{the leader}, that is responsible for a null controllability property; additionally, we have a control \textit{the…
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;…
This paper deals with the numerical computation of boundary null controls for the 1D wave equation with a potential. The goal is to compute an approximation of controls that drive the solution from a prescribed initial state to zero at a…
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 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…
It is by now well known that the use of Carleman estimates allows to establish the control-lability to trajectories of nonlinear parabolic equations. However, by this approach, it is not clear how to decide whether a given function is…
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 work addresses controllability properties for some systems of partial differential equations in which the main feature is the coupling through nonlocal integral terms. In the first part, we study a nonlinear parabolic-elliptic system…
This paper considers the controllability of a class of coupled Stokes systems with distributed controls. The coupling terms are of a different nature. The first coupling is through the principal part of the Stokes operator with a constant…
In this paper, we deal with the null controllability of a population dynamics model with an interior degenerate diffusion. To this end, we proved first a new Carleman estimate for the full adjoint system and afterwards we deduce a suitable…
In this paper we prove the null controllability of a one-dimensional degenerate parabolic equation with a weighted Robin boundary condition at the left endpoint, where the potential has a singularity. We use some results from the singular…
This article investigates the exact controllability of three-dimensional stochastic Maxwell equations, a coupled system comprising two stochastic partial differential equations. The research establishes the observability inequality for the…
This paper studies unique continuation for weakly degenerate parabolic equations in one space dimension. A new Carleman estimate of local type is obtained to deduce that all solutions that vanish on the degeneracy set, together with their…