Sensors and regional observability of the wave equation

The purpose of this paper is to develop the question of regional observability of a system described by the wave equation evolving in spatial domain Ω. It concerns the observability of such a system only on a subregion ω of Ω. Then we give definitions and characterization of this notion linked with sensors structure and we describe an important approach that estimates the state of the system on a given subregion. The study examines various kind of measurements and sensors. The obtained results are illustrated by numerical examples and simulations.