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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2014, Issue 1(34), Pages 48–55 (Mi vsgtu1289)  

This article is cited in 4 scientific papers (total in 4 papers)

Differential Equations

Problems with conjunction on a characteristic plane for the third-order hyperbolic equation in the three-dimensional space

I. N. Rodionova, V. M. Dolgopolov

Samara State University, Samara, 443100, Russian Federation

Abstract: In the present article the full equation of hyperbolic type of the third order with set of variable factors, in the area representing an infinite triangular prism, limited to the characteristic planes $z=0$, $x=h $ of the given equation and two noncharacteristic planes $y=x $, $y =-x $ is considered. Two boundary-value problems with data on the edges of the prism, which are both characteristic and non-characteristic planes of the given equation, are solved. In connection with difficulties of a gluing together of considered type solutions of the hyperbolic equations and the representation of conditions of interface on performance integrals and fractional derivatives have been introduced into interface conditions. On the interior characteristic plane the matching conditions, containing fractional order derivatives of required function, are established in order to avoid troubles with intersection of solutions. For equation considered in this article we have obtained the solution of the Darboux problem by method of Riemann, taken for the basis solutions of both problems, which are reduced to uniquely solvable equations of Volterra and Fredholm respectively, that has allowed to obtain the solutions of problems in the explicit analytic form.

Keywords: integral equations, boundary value problems, higher order hyperbolic type equations

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.909.2011
This research was carried within the framework of the State Assignment to Universities on Participation in carrying out Scientific Research (1.909.2011).


DOI: https://doi.org/10.14498/vsgtu1289

Full text: PDF file (579 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

Document Type: Article
UDC: 517.956.3
MSC: Primary 35L25; Secondary 35L35
Original article submitted 13/XI/2013
revision submitted – 23/I/2014

Citation: I. N. Rodionova, V. M. Dolgopolov, “Problems with conjunction on a characteristic plane for the third-order hyperbolic equation in the three-dimensional space”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(34) (2014), 48–55

Citation in format AMSBIB
\Bibitem{RodDol14}
\by I.~N.~Rodionova, V.~M.~Dolgopolov
\paper Problems with conjunction on a characteristic plane for the third-order hyperbolic equation in the three-dimensional space
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2014
\vol 1(34)
\pages 48--55
\mathnet{http://mi.mathnet.ru/vsgtu1289}
\crossref{https://doi.org/10.14498/vsgtu1289}
\zmath{https://zbmath.org/?q=an:06968824}
\elib{http://elibrary.ru/item.asp?id=22813959}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. V. Bushkov, I. N. Rodionova, “O postanovke odnoi nelokalnoi zadachi dlya uravneniya giperbolicheskogo tipa tretego poryadka”, Sovremennye problemy matematicheskikh i estestvennykh nauk v mire, Sbornik nauchnykh trudov po itogam mezhdunarodnoi nauchno-prakticheskoi konferentsii, Kazan, 2015, 18–22  elib
    2. S. V. Bushkov, I. N. Rodionova, “Nelokalnye zadachi dlya odnogo uravneniya giperbolicheskogo tipa tretego poryadka, vyrozhdayuschegosya na koordinatnykh ploskostyakh”, Science Time, 2016, no. 2 (26), 92–100  elib
    3. S. V. Bushkov, I. N. Rodionova, “Zadacha MN dlya odnogo uravneniya smeshannogo tipa s nestandartnymi usloviyami sopryazheniya”, Science Time, 2016, no. 5 (29), 103–110  elib
    4. O. A. Vasileva, I. N. Rodionova, “Dlya obobschennogo uravneniya Eilera-Darbu zadacha s nestandartnymi usloviyami sopryazheniya na kharakteristicheskoi linii”, Science Time, 2016, no. 5 (29), 116–124  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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