Carleman estimates for time-discrete parabolic equations and applications to controllability

Franck Boyer (1) , Víctor Hernández-Santamaría (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

In this paper, we prove a Carleman estimate for a time-discrete parabolic equation in which the large parameter is connected to the time step of the discretization scheme. This estimate is then used to obtain a relaxed observability estimate that yields some controllability results for linear and semi-linear time-discrete parabolic equations. We also discuss the application of this Carleman estimate to the controllability of coupled systems.

Mots clés: Carleman estimates; time-discrete heat equation; observability; null controllability

Domaines: Optimisation et contrôle [math.OC]

Franck Boyer, Víctor Hernández-Santamaría. Carleman estimates for time-discrete parabolic equations and applications to controllability. ESAIM: Control, Optimisation and Calculus of Variations, 2020, 26, ⟨10.1051/cocv/2019072⟩. ⟨hal-02121672⟩