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Potential theory for problems of diffraction on a layer between two parallel planes

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Abstract

We investigate the boundary-value problems that appear when studying the diffraction of acoustic waves on obstacles in a layer between two parallel planes. By using potential theory, these boundary-value problems are reduced to the Fredholm integral equations given on the boundary of the obstacles. The theorems on existence and uniqueness are proved for the Fredholm equations obtained and, hence, for the boundary-value problem.

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Authors and Affiliations

  1. Kiev University, Kiev

    Yu. K. Podlipenko

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  1. Yu. K. Podlipenko
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 5, pp. 647–662, May, 1993.

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Podlipenko, Y.K. Potential theory for problems of diffraction on a layer between two parallel planes. Ukr Math J 45, 706–723 (1993). https://doi.org/10.1007/BF01058207

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  • DOI: https://doi.org/10.1007/BF01058207

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