Hyperbolic Boundary Value Problem for Semibounded Piecewise-Homogeneous Hollow Cylinder

Автор(и)

  • Andrey Petrovich Gromyk State Agrarian and Engineering University in Podilya, Kamianets-Podilsky, Україна
  • Ivan Mykhaylovych I. Konet Kamianets-Podilskyi Ivan Ohiienko National University, Kamianets-Podilsky, Україна
  • Tatyana Mikhailovna Pylypiuk Kamianets-Podilskyi Ivan Ohiienko National University, Kamianets-Podilsky, Україна

DOI:

https://doi.org/10.32626/2308-5878.2018-17.22-33

Анотація

By means of the method of integral and hybrid integral transforms, in combination with the method of main solutions (influence matrices and Green matrices) the integral image of exact analytical solution of hyperbolic boundary value problem of mathematical physics for semibounded piecewise-homogeneous hollow cylinder is obtained for the first time.

Посилання

Hadamard J. The Cauchy problem for linear partial differential equations of parabolic type / J. Hadamard. — Moscow : Nauka, 1978. — 352 p.

Gording L. Cauchy's problem for hyperbolic equations / L. Gording. — Мoscow : IL, 1961. — 122 p.

Mytropol’skiy Yu. Asymptotic methods of investigation of quasi-wave equa-tions of hyperbolic type / Yu. Mytropol’skiy, G. Khoma, M. Gromiak. — Кyiv : Naukova Dumka, 1991. — 232 p.

Samoilenko A. Numerical-analytic methods in the theory of periodic solutions of partial differential equations / A. Samoilenko, B. Tkach. — Kyiv : Naukova Dumka, 1992. — 208 p.

Smirnov M. Degenerating elliptic and hyperbolic equations / M. Smirnov. — Мoscow : Nauka, 1962. — 292 p.

Cherniatyn V. Fourier method in mixed problem for partial differential equations / V. Cherniatyn. — Мoscow : Izd. MGU, 1991. — 112 p.

Sergienko I. Mathematic modeling and the study of processes in heterogeneous environments / I. Sergienko, V. Skopetsky, V. Deineka. — Kyiv : Naukova Dumka, 1991. — 432 p.

Deineka V. Models and methods of solving of problems with conjugate conditions / V. Deineka, I. Sergienko, V. Skopetsky. — Kyiv : Naukova Dumka, 1998. — 614 p.

Konet I. The temperature fields in the piece-homogeneous cylindrical domains / I. Konet, M. Leniuk. — Chernivtsi : Prut, 2004. — 276 p.

Gromyk A. The temperature fields in the piece-homogeneous spatial environments / A. Gromyk, I. Konet, M. Leniuk. — Kamenets-Podilsky : Abetka-Svit, 2011. — 200 p.

Konet I. Hyperbolic boundary-value problems of mathematical physics in piece-wise homogeneous spacial environments / I. Konet. — Kamenets-Podilsky : Abetka-Svit, 2013. — 120 p.

Konet I. Parabolic boundary value problems in piecewise homogeneous environments / I. Konet, T. Pylypiuk. — Kamenets-Podilsky : Abetka-Svit, 2016. — 244 p.

Gromyk A. Hyperbolic boundary value problem for semibounded piecewise-homogeneous solid cylinder / A. Gromyk, I. Konet, T. Pylypiuk // Mathematical and computer modelling. Series: Physics and Mathematics: scientific journal / Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kamianets-Podilsky National Ivan Ohienko University. — Kamianets-Podilsky : Kamianets-Podil. Nat. I. Ohienko Un., 2017. — Issue 16. — P. 48–59.

Perestiuk M. The theory of equations of mathematical physics / M. Perestiuk, V. Marynets’. — Kyiv : Lybid’, 2006. — 424 p.

Sneddon I. Fourier transforms / I. Sneddon. — Мoscow : IL, 1955. — 668 p.

Тranter К. Integral transformations in mathematical physics / К. Тranter. — Мoscow : Gostehteorizdat, 1956. — 204 p.

Bybliv O. Integral Hankel transform of the 2nd kind for piecewise-homogeneous segments / O. Bybliv, M. Lenyuk // News of univ. Mathemat-ics. — 1987. — № 5. — P. 82–85.

Shilov G. Mathematical analysis. Second special course / G. Shilov. — Moscow : Nauka, 1965. — 328 p.

Gelfand I. Some questions in the theory of differential equations / I. Gelfand, G. Shilov. — Мoscow : Fizmatgiz, 1958. — 274 p.

##submission.downloads##

Опубліковано

2018-05-18

Номер

2018: Математичне та комп'ютерне моделювання. Серія: Фізико-математичні науки. Випуск 17

Розділ

Статті

Ліцензія

Authors who publish with this journal agree to the following terms:

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).