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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 \(K\).

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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