Singular perturbation of reduced wave equation and scattering from an embedded obstacle

We consider time-harmonic wave scattering from an inhomogeneous isotropic medium supported in a bounded domain $\mathrm{\Omega }\subset {\mathbb{R}}^N$ ($N\ge 2$). {In a subregion $D⋐\mathrm{\Omega }$, the medium is supposed to be lossy and have a large mass density. We study the asymptotic development of the wave field as the mass density $\rho \to +\mathrm{\infty }$} and show that the wave field inside $D$ will decay exponentially while the wave filed outside the medium will converge to the one corresponding to a sound-hard obstacle $D⋐\mathrm{\Omega }$ buried in the medium supported in $\mathrm{\Omega }\mathrm{\backslash }\bar{D}$. Moreover, the normal velocity of the wave field on $\mathrm{\partial }D$ from outside $D$ is shown to be vanishing as $\rho \to +\mathrm{\infty }$. {We derive very accurate estimates for the wave field inside and outside $D$ and on $\mathrm{\partial }D$ in terms of $\rho$, and show that the asymptotic estimates are sharp. The implication of the obtained results is given for an inverse scattering problem of reconstructing a complex scatterer.}