no. 2
Distributed null controllability of some 1D cascade parabolic systems
Franck Boyer1 ; Morgan Morancey2
1Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS, UPS IMT, 31062 Toulouse Cedex 9, FRANCE
2Aix Marseille Univ, CNRS, I2M, UMR 7373, Marseille, FRANCE
Annales mathématiques Blaise Pascal, Tome 32 (2025) no. 2, pp. 221-280

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, 361:1191–1248, 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.

Publié le :
DOI : 10.5802/ambp.438
Classification : 93B05, 93C20, 35K40
Keywords: Control theory, parabolic partial differential equations, minimal null control time, block moment method

Franck Boyer  1   ; Morgan Morancey  2

1 Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS, UPS IMT, 31062 Toulouse Cedex 9, FRANCE
2 Aix Marseille Univ, CNRS, I2M, UMR 7373, Marseille, FRANCE
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Franck Boyer; Morgan Morancey. Distributed null controllability of some 1D cascade parabolic systems. Annales mathématiques Blaise Pascal, Tome 32 (2025) no. 2, pp. 221-280. doi: 10.5802/ambp.438

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