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Journal of Applied Mathematics
Volume 2015, Article ID 195460, 13 pages
Research Article

Multilayered Scattering Problem with Generalized Impedance Boundary Condition on the Core

1School of Mathematics and Statistics, South-Central University for Nationalities, 182 Minyuan Road, Wuhan 430074, China
2School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

Received 29 May 2015; Accepted 3 September 2015

Academic Editor: Carlos J. S. Alves

Copyright © 2015 Jun Guo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with the scattering problem of time-harmonic acoustic plane waves by an impenetrable obstacle buried in a piecewise homogeneous medium. The so-called generalized impedance boundary condition is imposed on the boundary of the obstacle. Firstly, the well posedness of the solution to the direct scattering problem is established by using the boundary integral method. Then a uniqueness result for the inverse scattering problem is proved; that is, both of the obstacle’s shape and the impedances (, ) can be uniquely determined from far field measurements. Furthermore, a mathematical basis is given to reconstruct the shape of the obstacle by using a modified linear sampling method.