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Dirichlet problem for axisymmetric potential fields in a disk of the meridian plane. I

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Ukrainian Mathematical Journal Aims and scope

Abstract

We develop new methods for the solution of boundary-value problems in the meridian plane of an antisymmetric potential solenoidal field with regard for the nature and specific features of axisymmetric problems. We determine the solutions of the Dirichlet problems for an axisymmetric potential and the Stokes flow function in a disk in an explicit form.

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References

  1. M. A. Lavrent’ev and B. V. Shabat, Problems of Hydrodynamics and Their Mathematical Models [in Russian] Nauka, Moscow 1977.

    Google Scholar 

  2. I. P. Mel’nichenko and S. A. Plaksa, “Potential fields with axial symmetry and algebras of monogenic functions of a vector variable. I,” Ukr. Mat. Zh., 48, No. 11. 1518–1529 (1996).

    Article  MathSciNet  Google Scholar 

  3. LP. Mel’nichenko and S. A. Plaksa, “Potential fields with axial symmetry and algebras of monogenic functions of a vector variable. II,” Ukr. Mat. Zh., 48, No. 12, 1695–1703 (1996).

    Article  MathSciNet  Google Scholar 

  4. I. P. Mel’nichenko and S. A. Plaksa, “Potential fields with axial symmetry and algebras of monogenic functions of a vector variable. III,” Ukr. Mat. Zh., 49, No. 2, 228–243 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  5. V. I. Smirnov, A Course in Higher Mathematics [in Russian], Vol. 2, Nauka. Moscow (1974).

    Google Scholar 

  6. V. I. Smimov, A Course in Higher Mathematics [in Russian], Vol. 3, Part 2, Nauka, Moscow (1969).

    Google Scholar 

  7. V. I. Smirnov, A Course in Higher Mathematics [in Russian], Vol. 4, Gostekhizdat, Moscow (1951).

    Google Scholar 

  8. C. Miranda, Partial Differential Equations of Elliptic Type [Russian translation] Inostrannaya Literatura, Moscow 1957.

    Google Scholar 

  9. S. G. Mikhlin, Linear Partial Differential Equations [in Russian] Vysshaya Shkola, Moscow 1977.

    Google Scholar 

  10. M. Brelot, Elements de la Theorie Classique du Potentiel [Russian translation] Mir, Moscow 1964.

    MATH  Google Scholar 

  11. L. G. Mikhailov and N. Radzhabov, “An analog of the Poisson formula for certain second-order equations with singular line,” Dokl. Akad. Nauk Tadzh. SSR, 15, No. 11, 6–9 (1972).

    Google Scholar 

  12. N. Radzhabov, “Construction of potentials and investigation of inner and outer boundary-value problems of Dirichlet and Neumann types for the Euler-Poisson-Darboux equations on a plane,” Dokl. Akad. Nauk Tadzh. SSR, 17, No. 8, 7–11 (1974).

    Google Scholar 

  13. L. G. Loitsyanskii, Mechanics of Liquids and Gases [in Russian] Nauka, Moscow 1987.

    Google Scholar 

  14. J. K. Batchelor, An Introduction to Fluid Dynamics [Russian translation] Mir, Moscow 1973.

    Google Scholar 

  15. I. I. Privalov, Boundary Properties of Analytic Functions [in Russian] Gostekhizdat, Moscow 1950.

    Google Scholar 

  16. F. D. Gakhov, Boundary-Value Problems [in Russian] Nauka, Moscow 1977.

    MATH  Google Scholar 

  17. M. A. Lavrent’ev and B. V. Shabat. Methods of the Theory of Functions of a Complex Variable [in Russian] Nauka, Moscow 1987.

    MATH  Google Scholar 

  18. N. Radzhabov. “Boundary-value problems for an equation of axisymmetric field theory,” in: Investigations of Boundary-Value Problems in the Theory of Functions and Differential Equations [in Russian], Academy of Sciences of Tadzhik SSR, Dushanbe (1965), pp. 79–128.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Ukranian Academy of Sciences, kiev

    S. A. Plaksa

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  1. S. A. Plaksa
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Plaksa, S.A. Dirichlet problem for axisymmetric potential fields in a disk of the meridian plane. I. Ukr Math J 52, 564–585 (2000). https://doi.org/10.1007/BF02515397

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  • DOI: https://doi.org/10.1007/BF02515397

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