Singular Perturbation of Reduced Wave Equation and Scattering from an Embedded Obstacle
Singular Perturbation of Reduced Wave Equation and Scattering from an Embedded Obstacle
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DOI：
10.1007/s10884-012-9270-5
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发表时间：
2011-11
影响因子：
1.3
通讯作者：
Hongyu Liu;Zaijiu Shang;Hongpeng Sun;J. Zou
中科院分区：
文献类型：
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作者：
Hongyu Liu;Zaijiu Shang;Hongpeng Sun;J. Zou
本文研究了在有界区域（N≥ 2）内支承的非均匀各向同性介质的时谐散射问题。在一个子区域中，介质被认为是有损耗的并且具有大的质量密度。本文研究了当质量密度ρ→ + ∞时波场的渐近发展，指出介质内部的波场将指数衰减，而介质外部的波场将收敛到介质中埋有声硬障碍物时的波场。当ρ→ + ∞时，从D外看，D上波场的法向速度为零。我们得到了关于ρ的Dand上的内外波场的非常精确的估计，并证明了渐近估计是尖锐的。所得结果的含义给出了重建一个复杂的散射体的逆散射问题。
We consider time-harmonic wave scattering from an inhomogeneous isotropic medium supported in a bounded domain(N≥ 2). In a subregion, 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 densityρ→ + ∞ and show that the wave field insideDwill decay exponentially while the wave filed outside the medium will converge to the one corresponding to a sound-hard obstacleburied in the medium supported in. Moreover, the normal velocity of the wave field on∂Dfrom outsideDis shown to be vanishing asρ→ + ∞. We derive very accurate estimates for the wave field inside and outsideDand on∂Din terms ofρ, 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.