Distributed null-controllability of some 1D cascade parabolic systems

Franck Boyer (1) , Morgan Morancey (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 I2M - Institut de Mathématiques de Marseille

We consider several coupled systems of one-dimensional linear parabolic equations where only one equation is controlled with a distributed control. For these systems we study the minimal null-control time that is the minimal time needed to drive any initial condition to zero. In a previous work [Comptes Rendus. Mathématique, Tome 361 (2023)] we extended the block moment method to obtain a complete characterization of the minimal null-control time in an abstract setting encompassing such non-scalar controls. In this paper, we push forward the application of this general approach to some classes of 1D parabolic systems with distributed controls whose analysis is out of reach by the usual approaches in the literature like Carleman-based methods, fictitious control and algebraic resolubility, or standard moment method. To achieve this goal, we need to prove refined spectral estimates for Sturm-Liouville operators that have their own interest.

Mots clés: Control theory; Parabolic partial differential equations; Minimal null control time; Block moment method

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Franck Boyer, Morgan Morancey. Distributed null-controllability of some 1D cascade parabolic systems. 2024. ⟨hal-03922940⟩