, Volume 24, Issue 4, pp 803-821

Singular Perturbation of Reduced Wave Equation and Scattering from an Embedded Obstacle

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Abstract

We consider time-harmonic wave scattering from an inhomogeneous isotropic medium supported in a bounded domain ${\Omega \subset \mathbb{R}^N}$ (N ≥ 2). In a subregion ${D \Subset \Omega}$ , 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 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 ${D \Subset \Omega}$ buried in the medium supported in ${\Omega \backslash \overline{D}}$ . 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.