Approximate acoustic cloaking in inhomogeneous isotropic space

We consider the approximate acoustic cloaking in an inhomogeneous isotropic background space. By employing transformation media, together with the use of a sound-soft layer lining right outside the cloaked region, we show that one can achieve the near-invisibility by the “blow-up-a-small-region” construction. This is based on novel scattering estimates corresponding to multiple multi-scale obstacles located in an isotropic space. We develop a novel system of integral equations to decouple the nonlinear scattering interaction among the small obstacle components, the regular obstacle components and the inhomogeneous background medium.