2025/02/21 by Hartman, Andreas, Koenig, Armand
#30H10 #30H20 #30J99 #35R11 #93C05 #93C20 #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2502.15532
In this paper we investigate null-controllable initial states of the half heat equation controlled from a sub-arc ω of the unit circle. We also study the projection on positive frequencies of the half-heat equation. For this projected half-heat equation, we obtain necessary as well as sufficient conditions for an initial condition to be null-controllable. These conditions, which are almost sharp, are expressed in term of projections on positive frequencies of functions supported on ω. From these results, and with the help of classical results on sum of holomorphic and anti-holomorphic functions, we also treat the (unprojected) half-heat equation. Surprisingly, without using our conditions on null-controllable states, we are able to show that the space of null-controllable functions does not depend on time by using a result of separation of singularities for holomorphic functions.