AbstractConsider the fluid-solid interaction problem for a two-layered non-penetrable cavity. We provide a novel fundamental proof for a uniqueness theorem on the determination of the interface between acoustic and elastic waves from many internal measurements, disregarding the boundary conditions imposed on the exterior non-penetrable boundary. The proof depends on a uniform {H^{1}}-norm boundedness for the elastic wave fields and the construction of the coupled interior transmission problem related to the acoustic and elastic wave fields.

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This paper is concerned with the inverse scattering of time-harmonic waves by a penetrable structure. By applying the integral equation method, we establish the uniform $L^{p}_{\alpha }\ (1< p\leq 2)$ L α p ( 1 < p ≤ 2 ) estimates for the scattered and transmitted wave fields corresponding to a series of incident point sources. Based on these a priori estimates and a mixed reciprocity relation, we prove that the penetrable structure can be uniquely identified by means of the scattered field measured only above the structure induced by a countably infinite number of quasi-periodic incident plane waves.

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In this paper, we consider the inverse scattering problem of determining a penetrable coated inhomogeneous dielectric with different kinds of unknown buried objects inside. The variational approach is adapted to show the well‐posedness of the direct scattering problem. For the inverse problem, we intend to reconstruct the shape and location of the coated dielectric from measured far‐field data by developing a modified factorization method. In fact, we shall first prove that the classical factorization method is effective for the case when a Neumann boundary condition is imposed on the buried object. However, for the case when a Dirichlet boundary condition is imposed on the buried object, the classical factorization method is no longer valid due to the loss of the coercivity of the middle operator of the associated factorization of the far‐field operator. In this case, we are expected to develop a modified factorization method to overcome this difficulty. Finally, some numerical examples are carried out to confirm the validity of the developed algorithms.

This paper is concerned with the inverse scattering of acoustic waves by an unbounded periodic elastic medium in the three-dimensional case. A novel uniqueness theorem is proved for the inverse problem of recovering a bi-periodic interface between acoustic and elastic waves using the near-field data measured only from the acoustic side of the interface, corresponding to a countably infinite number of quasi-periodic incident acoustic waves. The proposed method depends only on a fundamental a priori estimate established for the acoustic and elastic wave fields and a new mixed-reciprocity relation established in this paper for the solutions of the fluid-solid interaction scattering problem.

This paper is concerned with the inverse scattering of time-harmonic acoustic plane waves by a multi-layered fluid–solid medium in the three dimensional space. We establish the global uniqueness in identifying the embedded penetrable solid obstacle, the surrounding fluid medium and its wave number from the acoustic far-field pattern for all incident plane waves at a fixed frequency. The proof depends on constructing different kinds of interior transmission problems in appropriate small domains and the a priori estimates derived for both the elastic wave fields in the embedded solid obstacle and the acoustic wave fields in the surrounding fluid medium.