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Inverse problem for a perturbed stratified strip in two dimensions. (English) Zbl 1038.35158
Summary: We consider the divergence form elliptic operator \[ A=-\nabla_{x,z} \cdot (c^2(x,z)\nabla_{x,z}) \] in the strip \(\Omega = \mathbb R \times [0,H]\). The velocity \(c(x,z)\) describes the multistratification of \(\Omega\): a horizontal stratification with a compact perturbation \(K\), the velocity in \(K\) is an \(L^{\infty}(K)\) function. We suppose that the position of the perturbation is known and we prove uniqueness for identification of the perturbation from one generalized eigenfunction pattern in the neighbourhood of \(K\).

MSC:
35R30 Inverse problems for PDEs
35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
76Q05 Hydro- and aero-acoustics
35L05 Wave equation
35J25 Boundary value problems for second-order elliptic equations
47F05 General theory of partial differential operators
74J25 Inverse problems for waves in solid mechanics
86A22 Inverse problems in geophysics
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