Observability and sensors for hyperbolic systems

The wave equation defined on an open bounded regular domain n is considered. The measurement is obtained by means of a pointwise sensor located inside Ω The observability problem of the system is studied using the Hilbert Uniqueness Method developed by Lions and we show that it can be linked with the sensor structure. Morever we obtain from this approach, explicit formulae for the state to be reconstructed. These useful formulae are then implemented numerically and illustrated through two examples.