Related papers: Observability and null-controllability for parabol…
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…
The distributed null controllability for coupled parabolic systems with non-diagonalizable diffusion matrices with a reduced number of controls has been studied in the case of constant matrices. On the other hand, boundary controllability…
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 investigate a class of elliptic and parabolic partial differential equations driven by p(u) laplacian. This dependence necessitates the use of variable exponent Sobolev spaces specifically tailored to the anisotropic framework. For the…
In this paper, we are concerned with the internal control of a class of one-dimensional nonlinear parabolic systems with nonlocal and weakly degenerate diffusion coefficients. Our main theorem establishes a local null controllability result…
This paper is devoted to a study of the null controllability problems for one-dimensional linear degenerate wave equations through a boundary controller. First, the well-posedness of linear degenerate wave equations is discussed. Then the…
In this work, we study the controllability of the bilinear Schr\"odinger equation on infinite graphs for periodic quantum states. We consider the bilinear Schr\"odinger equation $i\partial_t\psi=-\Delta\psi+u(t)B\psi$ in the Hilbert space…
For linear infinite systems the approximate controllability problem by control constraints is considered. Controllability conditions represented via system parameters are obtained. Partial differential control systems and control systems…
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, a quadratic optimal control problem is considered for second-order parabolic PDEs with homogeneous Dirichlet boundary conditions, in which the "point" control function (depending only on time) constitutes a source term. These…
Let $\Om\subset\RR^N$ a bounded domain with a Lipschitz continuous boundary. We study the controllability of the space-time fractional diffusion equation \begin{equation*} \begin{cases} \mathbb D_t^\alpha u+(-\Delta)^su=0\;\;&\mbox{ in…
We prove the internal controllability of some systems of two coupled wave equations in one space dimension, with one control, under certain conditions on the coupling. To do this we apply the "fictitious control method" in two cases:…
In this paper, we study the observability and controllability of wave equations coupled by first or zero order terms on a compact manifold. We adopt the approach in Dehman-Lebeau's paper \cite{DehmanLebeau09} to prove that: the weak…
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…
Solutions of a system of wave equations are constructed for both homogeneous and inhomogeneous Dirichlet boundary conditions at every regularity level. We prove that boundary observability, and thus boundary exact controllability, at some…
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…
In this paper, we consider the wave equation with both a viscous Kelvin-Voigt and frictional damping as a model of viscoelasticity in which we incorporate an internal control with a moving support. We prove the null controllability when the…
This paper presents a new observability estimate for parabolic equations in $\Omega\times(0,T)$, where $\Omega$ is a convex domain. The observation region is restricted over a product set of an open nonempty subset of $\Omega$ and a subset…
We consider linear elliptic and parabolic equations with measurable coefficients and prove two types of $L_{p}$-estimates for their solutions, which were recently used in the theory of fully nonlinear elliptic and parabolic second order…
This paper deals with the hierarchical control of the parabolic equation.We use Stackelberg{Nash strategies. As usual, we consider one leader and two followers. To each leader we associate a Nash equilibrium corresponding to a bi-objective…