We prove new bounds on the control cost for the abstract heat equation, assuming a spectral
inequality or uncertainty relation for spectral projectors. In particular, we specify …

The advection-diffusion equation y ε t− εy ε xx+ My ε x= 0,(x, t)∈(0, 1)×(0, T) is null
controllable for any strictly positive values of the diffusion coefficient ε and of the …

In this paper, we prove explicit lower bounds for the cost of fast boundary controls for a class
of linear equations of parabolic or dispersive type involving the spectral fractional Laplace …

Let X,Y be Banach spaces, (S_t)_t≧0 a C_0-semigroup on X, -A the corresponding
infinitesimal generator on X, C a bounded linear operator from X to Y, and T>0. We consider …

In this paper, we study the cost of null controllability of a fourth-order parabolic equation.
When the control time is large enough, we prove that this cost decreases exponentially to …

The goal of this article is to provide a description of the reachable set of the one-dimensional
heat equation, set on the spatial domain x∈(-L,L) with Dirichlet boundary controls acting at …

In this article, we give a completely constructive proof of the observability/controllability of the
wave equation on a compact manifold under optimal geometric conditions. This contrasts …

We prove a scale-free, quantitative unique continuation principle for functions in the range of
the spectral projector χ (−∞, E](HL) of a Schrödinger operator HL on a cube of side L∈ ℕ …

We propose a method to establish the rapid stabilization of the bilinear Schr\" odinger
control system and its linearized system, and the finite time stabilization of the linearized …

We study the controllability properties of transport equations and of parabolic equations with
vanishing diffusivity posed on a tree-shaped network. Using a control localized on the …