DÍA / HORA: Jueves 17 de octubre 2024 / 16:30 – 17:30
EXPOSITOR: Sylvain Ervedoza, Institut de Mathématiques de Bordeaux, Université de Bordeaux and CNRS
RESUMEN: The goal of this talk is to explain how perturbative arguments can be applied to derive a sharp description of the reachable space for heat equations having lower order terms. The main result I will present is the following one. Let us consider an abstract system y’ = Ay + Bu, where A is an operator generating a C^0 semigroup (exp(tA))_{t ≥ 0} on a Hilbert space X, and B is a control operator, for instance a linear operator from an Hilbert space U to X, and let us assume that this system is null-controllable in X in any positive time. Then, setting R the reachable set of the system (that is all the states that can be achieved by y solution of y’ = Ay + Bu, y(0) = 0), the restriction of (exp(tA))_{t ≥ 0} to R forms a C^0 semigroup on R. Accordingly, the system y’ = Ay + Bu is exactly controllable on R, and one can then perform classical perturbative arguments to handle lower order terms, as I will explain on a few examples. This talk is based on a joint work with Kévin Le Balc’h (INRIA Paris) and Marius Tucsnak (Bordeaux). If time allows, I will also explain the strategy we develop in a recent work with Adrien Tendani-Soler (Bordeaux) to get a more refined description of the reachable space in the case of a ball controlled from its entire boundary, following the recent approach by Alexander Strohmaier and Alden Waters.
IDIOMA: English
LUGAR: Auditorio Ninoslav Bralic, Facultad de Matemática, Campus San Joaquín, Universidad Católica de Chile
DIRECCIÓN: Avda. Vicuña Mackenna 4860, Macul, Chile. Cómo llegar.
MODALIDAD: Presencial y transmisión por Microsoft Teams. Para acceder a la transmisión de la charla hacer click aquí.