We build nonuniform numerical meshes for the finite difference and finite element approximations of the one-dimensional wave equation, ensuring that all numerical solutions reach the boundary, as continuous solutions do, ...

In this article, we consider abstract linear conservative systems and their time-discrete counterparts. Our main result is a representation formula expressing solutions of the continuous model through the solution of the ...

In these Notes we make a self-contained presentation of the theory that has been developed recently for the numerical analysis of the controllability properties of wave propagation phenomena and, in particular, for the ...

The goal of this note is to explain how transmutation techniques (originally introduced in [14] in the context of the control of the heat equation, inspired on the classical Kannai transform, and recently revisited in [4] ...

The goal of this article is to derive new estimates for the cost of observability of heat equations. We have developed a new method allowing one to show that when the corresponding wave equation is observable, the heat ...

We prove a regularity result for an abstract control problem z' = Az + Bv with initial datum z(0) = z0 in which the goal is to determine a control v such that z(T) = 0. Under standard admissibility and observability ...

We consider time semi-discrete approximations of a class of exponentially stable infinite-dimensional systems modeling, for instance, damped vibrations. It has recently been proved that for time semi-discrete systems, due ...