Consider 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 -norm boundedness for the elastic wave fields and the construction of the coupled interior transmission problem related to the acoustic and elastic wave fields.
F. Cakoni, D. Colton and S. Meng,
The inverse scattering problem for a penetrable cavity with internal measurements,
Inverse Problems and Applications,
Contemp. Math. 615,
American Mathematical Society, Providence (2014), 71–88.
D. Colton, R. Kress and P. Monk,
Inverse scattering from an orthotropic medium,
J. Comput. Appl. Math. 81 (1997), no. 2, 269–298.
A. Kimeswenger, O. Steinbach and G. Unger,
Coupled finite and boundary element methods for fluid-solid interaction eigenvalue problems,
SIAM J. Numer. Anal. 52 (2014), no. 5, 2400–2414.
F. Qu, J. Yang and H. Zhang,
Shape reconstruction in inverse scattering by an inhomogeneous cavity with internal measurements,
SIAM J. Imaging Sci. 12 (2019), no. 2, 788–808.
J. Yang, B. Zhang and H. Zhang,
Uniqueness in inverse acoustic and electromagnetic scattering by penetrable obstacles with embedded objects,
J. Differential Equations 265 (2018), no. 12, 6352–6383.
This journal presents original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published.