Abstract

We consider the direct acoustic scattering problem with sound-hard scatterers. We discuss the stability of the solutions with respect to variations of the scatterer. The main tool we use for this purpose is the convergence in the sense of Mosco. As a consequence we obtain uniform decay estimates for scattered fields for a large class of admissible sound-hard scatterers. As a particular case, we show how a sound-hard screen may be approximated by thin sound-hard obstacles. This is a joint work with Giorgio Menegatti.

We show that a sound-hard screen may be also approximated by using a thin lossy layer. This is a crucial step, together with transformation optics, for the construction of approximate full and partial cloaking by inserting a lossy layer between the region to be cloaked and the observer. This is a joint work with Jingzhi Li, Hongyu Liu and Gunther Uhlmann.