The goal of this article is to analyze control properties of parabolic equations with a singular potential âˆ’Î¼/|x|, where Î¼ is a real number. When Î¼ â‰¤ (N âˆ’2)/4, it was proved in [19] that the equationâ€¦ (More)

Abstract In this article, we extensively develop Carleman estimates for the wave equation and give some applications. We focus on the case of an observation of the flux on a part of the boundaryâ€¦ (More)

In this article, we derive uniform admissibility and observability properties for the finite element space semi-discretizations of Ã¼ + A0u = 0, where A0 is an unbounded self-adjoint positive definiteâ€¦ (More)

In this article, we derive uniform admissibility and observability properties for the finite element space semi-discretizations of iÅ¼ = A0z, where A0 is an unbounded self-adjoint positive definiteâ€¦ (More)

The goal of this article is to analyze the observability properties for a space semi-discrete approximation scheme derived from a mixed finite element method of the 1d wave equation on nonuniformâ€¦ (More)

In this Note, we consider the 1-dimensional wave equation, discretized by means of Glimmâ€™s random choice method. We prove that for almost every choice of the random parameter, the observabilityâ€¦ (More)

Abstract. It is by now well known that one can recover a potential in the wave equation from the knowledge of the initial waves, the boundary data, and the flux on a part of the boundary satisfyingâ€¦ (More)

Using uniform global Carleman estimates for semi-discrete elliptic and hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in aâ€¦ (More)

In these Notes we make a self-contained presentation of the t heory that has been developed recently for the numerical analysis of th e controllability properties of wave propagation phenomena and,â€¦ (More)

In this article, we focus on the analysis of discrete versions of the CalderÃ³n problem in dimension d â‰¥ 3. In particular, our goal is to obtain stability estimates for the discrete CalderÃ³n problemsâ€¦ (More)