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Hyperbolic Boundary-Value Problem for a Piecewise Homogeneous Hollow Cylinder

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Ukrainian Mathematical Journal Aims and scope

By the method of integral and hybrid integral transforms in combination with the method of principal solutions (matrices of influence and Green matrices), we construct the integral representation of the unique exact analytic solution of a hyperbolic boundary-value problem of mathematical physics for a piecewise homogeneous hollow cylinder.

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References

  1. J. Hadamard, Le Probème de Cauchy et les Équations aux Dériveés Partielles Linéaires Hyperboliques, Herman, Paris (1932).

    MATH  Google Scholar 

  2. L. Gårding, Cauchy’s Problem for Hyperbolic Equations, University of Chicago (1957).

  3. Yu. A. Mitropol’skii, G. P. Khoma, and M. I. Gromyak, Asymptotic Methods for the Investigation of Quasiwave Hyperbolic Equations [in Russian], Naukova Dumka, Kiev (1991).

    Google Scholar 

  4. B. I. Ptashnyk, V. S. Il’kiv, I. Ya. Kmit’, and V. M. Polishchuk, Nonlocal Boundary-Value Problems for Partial Differential Equations [in Ukrainian], Naukova Dumka, Kyiv (2002).

  5. A. M. Samoilenko and B. P. Tkach, Numerical-Analytic Methods in the Theory of Periodic Solutions of Partial Differential Equations [in Russian], Naukova Dumka, Kiev (1992).

    Google Scholar 

  6. M. M. Smirnov, Degenerating Elliptic and Hyperbolic Equations [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  7. V. A. Chernyatin, Substantiation of the Fourier Method in Mixed Problems for Partial Differential Equations [in Russian], Moscow University, Moscow (1991).

    Google Scholar 

  8. I. V. Sergienko, V. V. Skopetskii, and V. S. Deineka, Mathematical Simulation and Investigation of the Processes in Inhomogeneous Media [in Russian], Naukova Dumka, Kiev (1991).

    Google Scholar 

  9. V. S. Deineka, I. V. Sergienko, and V. V. Skopetskii, Models and Methods for the Solution of Problems with Conjugation Conditions [in Russian], Naukova Dumka, Kiev (1998).

    Google Scholar 

  10. V. S. Deineka and I. V. Sergienko, Models and Methods for the Solution of Problems in Inhomogeneous Media [in Russian], Naukova Dumka, Kiev (2001).

    Google Scholar 

  11. I. M. Konet and M. P. Lenyuk, Stationary and Nonstationary Temperature Fields in Cylindrically Circular Domains [in Ukrainian], Prut, Chernivtsi (2001).

    Google Scholar 

  12. A. P. Hromyk, I. M. Konet, and M. P. Lenyuk, Temperature Fields in Piecewise Homogeneous Space Media [in Ukrainian], Abetka-Svit, Kam’yanets’-Podil’skyi (2011).

    Google Scholar 

  13. I. M. Konet, Hyperbolic Boundary-Value Problems of Mathematical Physics in Piecewise Homogeneous Space Media [in Ukrainian], Abetka-Svit, Kam’yanets’-Podil’skyi (2013).

    Google Scholar 

  14. I. M. Konet and T. M. Pylypyuk, Parabolic Boundary-Value Problems in Piecewise Homogeneous Media [in Ukrainian], Abetka-Svit, Kam’yanets’-Podil’skyi (2016).

    Google Scholar 

  15. A. P. Hromyk, I. M. Konet, and T. M. Pylypyuk, “Hyperbolic boundary-value problem for a piecewise homogeneous cylindricalcircular layer,” Visn. Kyiv. Nats. Univ., Ser. Mat. Mekh., Issue 1(39), 19–25 (2018).

  16. A. P. Hromyk, I. M. Konet, and T. M. Pylypyuk, “Hyperbolic boundary-value problem for a piecewise homogeneous cylindricalcircular layer with a hollow,” Visn. Kyiv. Nats. Univ., Ser. Mat. Mekh., Issue 1(39), 25–28 (2018).

  17. I. M. Konet and T. M. Pylypyuk, “Hyperbolic boundary-value problem for a piecewise homogeneous solid cylinder,” Nelin. Kolyv., 21, No. 4, 485–495 (2018).

    MathSciNet  Google Scholar 

  18. M. O. Perestyuk and V. V. Marynets’, Theory of Equations of Mathematical Physics [in Ukrainian], Lybid’, Kyiv (2006).

    Google Scholar 

  19. C. J. Tranter, Integral Transforms in Mathematical Physics, New York, Wiley (1954).

    MATH  Google Scholar 

  20. O. Ya. Bybliv and M. P. Lenyuk, “Hybrid integral Hankel transformations of the second kind for piecewise homogeneous segments,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No 5, 82–85 (1987).

  21. G. E. Shilov, Mathematical Analysis. Second Special Course [in Russian], Nauka, Moscow (1965).

    Google Scholar 

  22. I. M. Gelfand and G. E. Shilov, Some Problems of the Theory of Differential Equations [in Russian], Fizmatgiz, Moscow (1958).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Podil’skyi State Agrarian Technical University, Kam’yanets’-Podil’skyi, Ukraine

    A. P. Gromyk

  2. Ohienko Kam’yanets’-Podil’skyi National University, Kam’yanets’-Podil’skyi, Ukraine

    I. M. Konet & T. M. Pylypiuk

Authors
  1. A. P. Gromyk
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  2. I. M. Konet
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  3. T. M. Pylypiuk
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Corresponding author

Correspondence to I. M. Konet.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 12, pp. 1607–1617, December, 2019.

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Gromyk, A.P., Konet, I.M. & Pylypiuk, T.M. Hyperbolic Boundary-Value Problem for a Piecewise Homogeneous Hollow Cylinder. Ukr Math J 71, 1843–1854 (2020). https://doi.org/10.1007/s11253-020-01751-8

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  • DOI: https://doi.org/10.1007/s11253-020-01751-8

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