Related papers: Stabilization and controllability of first-order i…
In this paper, we study the exact controllability and stabilization of a system of two wave equations coupled by velocities with an internal, local control acting on only one equation. We distinguish two cases. In the first one, when the…
We discuss stabilization around trajectories of the continuity equation with nonlocal vector fields, where the control is localized, i.e., it acts on a fixed subset of the configuration space. We first show that the correct definition of…
A possible definition of strong/symmetric hyperbolicity for a second-order system of evolution equations is that it admits a reduction to first order which is strongly/symmetric hyperbolic. We investigate the general system that admits a…
The paper puts forward sufficient conditions for local controllability of a control dynamical system. The results obtained are meaningful in the case when the linear approximation to this system is not completely controllable. As a…
The present paper provides a sufficient condition to ensure output finite-time and fixed-time stability. Comparing with analogous researches the proposed result is less restrictive and obtained for a wider class of systems. The presented…
In this paper we prove a uniform controllability result for a fourth order parabolic partial differential equation which includes a transport term, when the coefficients of higher order terms vanish. We prove the null controllability of the…
We consider the problem of stabilization to zero of semilinear normal parabolic equations connected with the 3D Helmholtz system with periodic boundary conditions and arbitrary initial datum. This problem was previously studied in…
For a symmetric hyperbolic system of the first order, we prove a Carleman estimate under some positivity condition concerning the coefficient matrices. Next, applying the Carleman estimate, we prove an observability $L^2$-estimate for…
It is first shown that a smooth controllable system on a compact manifold is finite time controllable. The technique of proof is close to the one of Sussmann's orbit theorem, and no rank condition is required. This technique is also used to…
This study presents an efficient, accurate, effective and unconditionally stable time stepping scheme for the Darcy-Brinkman equations in double-diffusive convection. The stabilization within the proposed method uses the idea of stabilizing…
In this paper, we study the local exact boundary controllability of entropy solutions to a class linearly degenerate hyperbolic systems of conservation laws with constant multiplicity. The authors prove the two-sided boundary…
The moment method is used to prove the exact controllability of a wide class of bidimensional linear dispersive PDE's posed on the two-dimensional torus $\mathbb{T}^{2}.$ The control function is considered to be acting on a small vertical…
We establish a link between stability estimates for a hyperbolic inverse problem via the Boundary Control method and the blowup of a constant appearing in the contexts of optimal unique continuation and cost of approximate controllability.
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
The present work is concerned with the stabilization of a general class of time-varying linear parabolic equations by means of a finite-dimensional receding horizon control (RHC). The stability and suboptimality of the unconstrained…
For linear control systems in discrete time controllability properties are characterized. In particular, a unique control set with nonvoid interior exists and it is bounded in the hyperbolic case. Then a formula for the invariance pressure…
We consider a space-time variational formulation of the second-order wave equation, where integration by parts is also applied with respect to the time variable. Conforming tensor-product finite element discretisations with piecewise…
An integro-differential equation of hyperbolic type, with mixed boundary conditions, is considered. A continuous space-time finite element method of degree one is formulated. A posteriori error representations based on space-time cells is…
The paper addresses the boundary control of a class of hyperbolic PDEs, based on an equivalent representation in terms of an integral-difference equation. The situation is considered where direct compensation of reflection terms induces a…
In this paper we consider the controllability of certain class of non-autonomous neutral evolution stochastic functional differential equations, with time varying delays, driven by a fractional Brownian motion in a separable real Hilbert…