Date/heure
9 mars 2018
11:00 - 12:00
Oratrice ou orateur
Jérôme Lohéac
Catégorie d'évènement Séminaire EDP, Analyse et Applications (Metz)
Résumé
The heat equation with homogeneous Dirichlet boundary conditions is well known to preserve non-negativity. Besides, due to infinite velocity of propagation, the heat equation is null-controllable within arbitrary small time, with controls supported in any arbitrarily open subset of the domain (or its boundary) where heat diffuses. The following question then arises naturally: can the heat dynamics be controlled from a positive initial steady-state to a positive final one, requiring that the state remains nonnegative along the controlled time-dependent trajectory? I will show that this state-constrained controllability property can be achieved if the control time is large enough, but that it fails to be true in general if the control time is too short, thus showing the existence of a positive minimal controllability time. In other words, in spite of infinite velocity of propagation, realizing controllability under the unilateral non-negativity state constraint requires a positive minimal time