Carleman estimates and distribution of resonances for the transparent obstacle and application to the stabilization

The purpose of this paper is to study the resonances associated to the transparent obstacles. We prove the existence of an exponentially small neighborhood of the real axis free from the poles of the resolvent. As an application of these results, we get information about decay‐speed of the local energy. We prove that for regular data, the energy decays at least as fast as the inverse of the logarithm of the time.