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Reconstruction of penetrable obstacles in the anisotropic acoustic scattering

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  • We develop an enclosure-type reconstruction scheme to identify penetrable obstacles in acoustic waves with anisotropic medium in $\mathbb{R}^{3}$. The main difficulty of treating this problem lies in the fact that there are no complex geometrical optics solutions available for the acoustic equation with anisotropic medium in $\mathbb{R}^{3}$. Instead, we will use another type of special solutions called oscillating-decaying solutions. Even though that oscillating-decaying solutions are defined only on the half space, we are able to give necessary boundary inputs by the Runge approximation property. Moreover, since we are considering a Helmholtz-type equation, we turn to Meyers' $L^{p}$ estimate to compare the integrals coming from oscillating-decaying solutions and those from reflected solutions.
    Mathematics Subject Classification: Primary: 35R30; Secondary: 35J15.


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