6 papers
Optimal cost of fast boundary controls for the one-dimensional heat equation
Pierre Lissy
We consider the heat equation on with homogeneous Dirichlet condition at one endpoint and a Dirichlet boundary control at the other. If \(C_{\mathrm H}(T,L)\) denotes the o…
Control and stabilization of cascade coupled systems: application to a 1-d heat and wave coupled system
Lucas Davron, Pierre Lissy, Swann Marx
We study cascade coupled systems, for which our prototypical example is a 1-d heat equation coupled with a 1-d wave equation. The heat component is controlled through one boundary…
Traffic Flow Reconstruction from Limited Collected Data
Nail Baloul, Amaury Hayat, Thibault Liard +1
We propose an efficient method for reconstructing traffic density with low penetration rate of probe vehicles. Specifically, we rely on measuring only the initial and final positio…
Exact output tracking for the one-dimensional heat equation and applications to the interpolation problem in Gevrey classes of order 2
Lucas Davron, Pierre Lissy
This paper provides a complete characterization of the Dirichlet boundary outputs that can be exactly tracked in the one-dimensional heat equation with Neumann boundary control. Th…
Null controllability of the 1D heat equation with interior inverse square potential
Pierre Lissy, Tanguy Lourme
This paper aims to answer an open problem posed by Morancey in 2015 concerning the null controllability of the heat equation on (-1, 1) with an internal inverse square potential lo…
Effective multipliers for weights whose log are Hölder continuous. Application to the cost of fast boundary controls for the 1D Schr{ö}dinger equation
Pierre Lissy
We give a simple proof of the Beurling-Malliavin multiplier theorem (BM1) in the particular case of weights that verify the usual finite logarithmic integral condition and such tha…