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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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