1111.2444 (Hongyu Liu et al.)

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

Hongyu Liu, Zaijiu Shang, Hongpeng Sun, Jun Zou

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.}

View original: http://arxiv.org/abs/1111.2444