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Hilbert Boundary-Value Problem With Two-Side Curling at Infinity Point of Different Orders

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Abstract

We study a boundary-value problem for a generalized biaxisymmetric Helmholtz equation. Boundary conditions in this problem depend on equation parameters. By the method of separation of variables, using the Fourier-Bessel series expansion and the Hankel transform, we prove the unique solvability of the problem and establish explicit formulas for its solution.

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Acknowledgments

Supported by Russian Foundation for Basic Research, grants No. No. 17-01-00282-a, 18-31-00060.

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Authors and Affiliations

  1. Kazan State Architecture and Civil Engineering University, ul. Zelyonaya 1, Kazan, 420043, Russia

    E. N. Khasanova & P. L. Shabalin

Authors
  1. E. N. Khasanova
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  2. P. L. Shabalin
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Corresponding authors

Correspondence to E. N. Khasanova or P. L. Shabalin.

Additional information

Russian Text © E.N. Khasanova, P.L. Shabalin, 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 3, pp. 38–53.

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Khasanova, E.N., Shabalin, P.L. Hilbert Boundary-Value Problem With Two-Side Curling at Infinity Point of Different Orders. Russ Math. 63, 31–44 (2019). https://doi.org/10.3103/S1066369X19030046

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  • DOI: https://doi.org/10.3103/S1066369X19030046

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