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Well-posedness of the poincaré problem in a cylindrical domain for the higher-dimensional wave equation

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Abstract

It is known that waves (acoustic waves, radio waves, elastic waves, and electric waves) in cylindrical tubes are described by the wave equation. In the theory of hyperbolic-type partial differential equations, boundary-value problems with data on the whole boundary serve as examples of ill-posedness of the posed problems. In this work, it is shown that the Poincar´e problem in a cylindrical domain for the higher-dimensional wave equation is uniquely solvable. A uniqueness criterion for a regular solution is also obtained.

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Authors and Affiliations

  1. Aktobe State University, Aktobe, Kazakhstan

    S. A. Aldashev

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  1. S. A. Aldashev
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Correspondence to S. A. Aldashev.

Additional information

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 67, Partial Differential Equations, 2010.

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Aldashev, S.A. Well-posedness of the poincaré problem in a cylindrical domain for the higher-dimensional wave equation. J Math Sci 173, 150–154 (2011). https://doi.org/10.1007/s10958-011-0236-7

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  • DOI: https://doi.org/10.1007/s10958-011-0236-7

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