Singular Perturbation of Reduced Wave Equation and Scattering from an Embedded Obstacle |
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Authors: | Hongyu Liu Zaijiu Shang Hongpeng Sun Jun Zou |
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Institution: | 1. Department of Mathematics and Statistics, University of North Carolina, Charlotte, NC, 28263, USA 2. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China 3. Department of Mathematics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong
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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. |
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