Analysis of the controllability from the exterior of strong damping nonlocal wave equations

Warma, Mahamadi; Zamorano, Sebastián

ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 42.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

We make a complete analysis of the controllability properties from the exterior of the (possible) strong damping wave equation associated with the fractional Laplace operator subject to the non-homogeneous Dirichlet type exterior condition. In the first part, we show that if 0 < s < 1, $$ (N ≥ 1) is a bounded Lipschitz domain and the parameter δ > 0, then there is no control function g such that the following system

$$

is exact or null controllable at time T > 0. In the second part, we prove that for every δ ≥ 0 and 0 < s < 1, the system is indeed approximately controllable for any T > 0 and $$, where $$ is any non-empty open set.

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