We are pleased to announce a Talk on Tuesday, September 22nd, at 16:00, at Seminarraum 01.779, Staudtstraße 7, Erlangen. The talk, titled “Minimum time for the approximate controllability of some non-linear Schrödinger and wave equations with bilinear finite-dimensional controls” will be presented by Eugenio Pozzoli, Institut Recherche Mathématique de Rennes.
This event is open to all and is organized and hosted by Davide Lonigro.
Abstract of the talk
In this talk, I will present some recent results on the bilinear control of some partial differential equations. Our geometric technique, based on “Lie bracket” arguments and actions of diffeomorphisms groups on densities, permit to give new information on (and in some cases completely characterize) the minimum time needed for global approximate controllability. We shall focus on Schrödinger and wave equations posed on tori or euclidean spaces, but such techniques actually apply to many other PDE systems posed on a general manifold with bilinear or linear structure in the control. In particular, in the talk I will present two results: (i) for some Schrödinger equations the minimum control time for global L^2-approximate controllability is zero, independently of the initial state of the system, and (ii) for some wave equations, due to finite speed of propagation, the minimum control time for global H^1 x L^2-approximate controllability coincides with the maximum radius of a ball contained in the zero set of the initial state. The talk will be based on the article [1] and the preprint [2] in collaboration with Karine Beauchard and Thomas Perrin (École Normale Supérieure de Rennes, France).
[1] Karine Beauchard, Eugenio Pozzoli; Small-time approximate controllability of bilinear Schrödinger equations and diffeomorphisms. Ann. Inst. Henri Poincaré C Anal. Non Linéaire (2025), published online first.
[2] Karine Beauchard, Thomas Perrin, Eugenio Pozzoli; Approximate controllability of a bilinear wave equation and minimum time. (2026) arXiv:2601.19544