Boundary null-controllability of coupled parabolic systems with Robin conditions

Kuntal Bhandari (1) , Franck Boyer (1, 2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IUF - Institut universitaire de France

The main goal of this paper is to investigate the boundary controllability of a coupled parabolic system in the cascade form in the case where the boundary conditions are of Robin type. In particular, we prove that the associated controls satisfy suitable uniform bounds with respect to the Robin parameters, that let us show that they converge towards a Dirichlet control when the Robin parameters go to infinity. This is a justification of the popular penalisation method for dealing with Dirichlet boundary data in the framework of the controllability of coupled parabolic systems.

Mots clés: parabolic systems; Control theory; moments method; spectral estimates 9 AMS subject classifications 35B30 -35K20 -93B05 10; spectral estimates.

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

Kuntal Bhandari, Franck Boyer. Boundary null-controllability of coupled parabolic systems with Robin conditions. 2019. ⟨hal-02091091v1⟩