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Inverse problem of acoustic scattering in a space with a local inhomogeneity

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Abstract

An inclusion of finite size with a variable wave propagation velocity is contained in a homogeneous space. It is exposed to plane waves being propagated in all possible directions. The inverse problem is to restore the velocity by means of the scattering amplitude which is determined in terms of the scattered wave asymptotic for large ∥x∥. A procedure for restoration is described and a uniqueness theorem is presented in the paper.

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Authors
  1. M. I. Belishev
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  2. Ya. V. Kurylev
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 156, pp. 24–34, 1986.

The authors are deeply grateful to the participants of the A. S. Blagoveschenskii seminar for valuable comments and discussion.

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Belishev, M.I., Kurylev, Y.V. Inverse problem of acoustic scattering in a space with a local inhomogeneity. J Math Sci 50, 1696–1702 (1990). https://doi.org/10.1007/BF01097098

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  • DOI: https://doi.org/10.1007/BF01097098

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