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 ⊂ RN (N ≥ 2). In a subregion D , 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 ρ → +∞ 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 buried in the medium supported in \D. Moreover, the normal velocity of the wave field on ∂D from outside D is shown to be vanishing as ρ → +∞. We derive very accurate estimates for the wave field inside and outside D and on ∂D in terms of ρ, 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.