This paper is concerned with inverse acoustic scattering in an inhomogeneous medium with a conductive boundary condition and the unknown buried impenetrable objects inside. Using a variational approach, we establish the well-posedness of the direct problem. For the inverse problem, we shall numerically reconstruct the inhomogeneous medium from the far-field data for different kinds of cases. For the case when a Dirichlet boundary condition is imposed on the buried object, the classical factorization method proposed in [2] is justified as valid for reconstructing the inhomogeneous medium from the far-field data. For the case when a Neumann boundary condition is imposed on the buried object, the classical factorization method of [1] cannot be applied directly, since the middle operator of the factorization of the far-field operator is only compact. In this case, we develop a modified factorization method to locate the inhomogeneous medium with a conductive boundary condition and the unknown buried objects. Some numerical experiments are provided to demonstrate the practicability of the inversion algorithms developed.
Fenglong Qu
,
Ruixue Jia
,
Yanli Cui
. INVERSE CONDUCTIVE MEDIUM SCATTERING WITH UNKNOWN BURIED OBJECTS*[J]. Acta mathematica scientia, Series B, 2023
, 43(5)
: 2005
-2025
.
DOI: 10.1007/s10473-023-0505-9
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