Analysis & Applied Math

Event Information On the reachable space of the heat equation
14:10 on Friday February 10, 2023
15:00 on Friday February 10, 2023
BA6183, Bahen Center, 40 St. George St.
Marcu-Antone Orsoni

University of Toronto Mississauga

It is well-known that the heat equation is not exactly controllable from the boundary because of the smoothing effect of its kernel. One can then ask which states are reachable at a given time. In this talk, we will give a definitive description of the reachable set of the one-dimensional heat equation on a segment as the Bergman space of a certain square. This result involves complex and harmonic analysis tools as a separation of singularities theorem for the Bergman space. Finally, we will give an overview of the open problems related to this result. This talk is based on joint works with Andreas Hartmann.