Hyperbolic Boundary Value Problem for Unlimited Piecewise-Homogeneous Hollow Cylinder

Автор(и)

  • Іван Михайлович Конет Кам'янець-Подільський національний університет імені Івана Огієнка, Ukraine
  • Тетяна Михайлівна Пилипюк Кам'янець-Подільський національний університет імені Івана Огієнка, Ukraine

DOI:

https://doi.org/10.32626/2308-5878.2016-14.91-101

Анотація

By means of the method of integral and hybrid integral transforms, in combination with the method of main solutions (influence functions and Green functions) the integral image of exact analytical solution of hyperbolic boundary value problem of mathematical physics for unlimited 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.

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

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

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

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

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

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

Deineka V. Models and methods of solving of problems with conjugate condi-tions / V. Deineka, I. Sergienko, V. Skopetsky. — Kyiv : Naukova Dumka, 1998.

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

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

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

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

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

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

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

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

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

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

##submission.downloads##

Опубліковано

2016-07-27