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Boundary-value problems for Helmholtz equations in an angular domain. I

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Abstract

The boundary-value problems are investigated that arise when studying the diffraction of acoustic waves on an infinite cylinder with cross-section of an arbitrary shape situated inside a wedge so that the axis of the cylinder is parallel to the edge of the wedge. The potential theory is worked out which enables one to reduce these boundary-value problems to integral equations on a one-dimensional contour — the boundary of the cross-section of this cylinder. The theorems on existence and uniqueness of solutions to the boundary-value problems and the corresponding integral equations are proved. For this case, a principle of limit absorption is established. Effective algorithms for calculating the kernels of the integral operators are constructed.

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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. 3, pp. 403–418, March, 1993.

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Podlipenko, Y.K. Boundary-value problems for Helmholtz equations in an angular domain. I. Ukr Math J 45, 430–447 (1993). https://doi.org/10.1007/BF01061016

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  • DOI: https://doi.org/10.1007/BF01061016

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