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Asymptotics of solutions of spectral problems of hydrodynamics in the neighborhood of angular points

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Abstract

At angular points on the boundary of a domain, we obtain an asymptotic expansion for the eigenfunctions of spectral problems that describe natural oscillations of an ideal liquid that partially fills a cavity in a solid body. We describe cases where the eigenfunctions have singularities at angular points.

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References

  1. V. A. Kondrat’ev, “Boundary-value problems for elliptic equations in domains with conic or angular points/*,” Tr. Mosk. Mat. Obshch., 16, 209–292 (1967).

    MATH  Google Scholar 

  2. A. N. Komarenko, “Asymptotic expansion of eigenfunctions of a problem with a parameter in boundary conditions in the neighborhood of angular limit points,” Ukr. Mat. Zh., 32, No. 6, 653–659 (1980).

    MATH  MathSciNet  Google Scholar 

  3. S. A. Nazarov and B. A. Plamenevskii, Elliptic Problems in Domains with Piecewise-Smooth Boundary [in Russian], Nauka, Moscow (1991).

    Google Scholar 

  4. I. A. Lukovskii, M. Ya. Barnyak, and A. N. Komarenko, Approximate Methods for the Solution of Problems of Dynamics of a Limited Volume of Liquid [in Russian], Naukova Dumka, Kiev (1984).

    Google Scholar 

  5. N. D. Kopachevskii, S. G. Krein, and Ngo Zui Kan, Operator Methods in Linear Hydrodynamics [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  6. I. A. Lukovskii, Introduction to Nonlinear Dynamics of Solid Bodies with Cavities Filled with Liquid [in Russian], Naukova Dumka, Kiev (1990).

    Google Scholar 

  7. Yu. M. Berezanskii, Expansion in Eigenfunctions of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965).

    Google Scholar 

  8. A. N. Komarenko, “Eigenvalue problem with a parameter in boundary conditions for elliptic equations that degenerate on a part of the boundary of a domain,” Ukr. Mat. Zh., 18, No. 6, 3–11 (1966).

    MATH  MathSciNet  Google Scholar 

  9. S. L. Sobolev, Some Applications of Functional Analysis in Mathematical Physics [in Russian], Nauka, Moscow (1988).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    O. N. Komarenko

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  1. O. N. Komarenko
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 6, pp. 803–811, June, 1998.

This work was partially supported by the Ukrainian State Committee on Science and Technology.

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Komarenko, O.N. Asymptotics of solutions of spectral problems of hydrodynamics in the neighborhood of angular points. Ukr Math J 50, 912–921 (1998). https://doi.org/10.1007/BF02515224

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  • DOI: https://doi.org/10.1007/BF02515224

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