Mathematics – Analysis of PDEs
Scientific paper
2011-11-10
Mathematics
Analysis of PDEs
Scientific paper
We consider time-harmonic wave scattering from an inhomogeneous isotropic medium supported in a bounded domain $\Omega\subset\mathbb{R}^N$ ($N\geq 2$). {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 $\rho\rightarrow +\infty$} 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 $D\Subset\Omega$ 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 $\rho\rightarrow +\infty$. {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.}
Liu Hongyu
Shang Zaijiu
Sun Hongpeng
Zou Jun
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