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

Abstract

We consider time-harmonic wave scattering from an inhomogeneous isotropic medium supported in a bounded domain $\Omega \subset {\mathbb{R}}^N$ ($N\ge 2$). {In a subregion $D⋐\Omega$, 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 $\rho \to +\infty$} 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 $D⋐\Omega$ buried in the medium supported in $\Omega \backslash \bar{D}$. Moreover, the normal velocity of the wave field on $\partial D$ from outside $D$ is shown to be vanishing as $\rho \to +\infty$. {We derive very accurate estimates for the wave field inside and outside $D$ and on $\partial D$ 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.}

References in corpus (1)

• Virtual reshaping and invisibility in obstacle scattering

Cited by in corpus (7)

• Regularized Transformation-Optics Cloaking for the Helmholtz Equation: From Partial Cloak to Full Cloak
• Recovery of an embedded obstacle and its surrounding medium by formally-determined scattering data
• A Newton method for simultaneous reconstruction of an interface and a buried obstacle from far-field data
• A novel quantitative inverse scattering scheme using interior resonant modes
• Regularized Transformation-Optics Cloaking in Acoustic and Electromagnetic Scattering
• Uniqueness of scatterer in inverse acoustic obstacle scattering with a single incident plane wave
• Uniqueness in Determining Refractive Indices by Formally-determined Far-field Data