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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.], 2016, Volume 20, Number 1, Pages 7–21 (Mi vsgtu1452)  

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

Differential Equations and Mathematical Physics

Goursat problem for loaded degenerate second order hyperbolic equation with Gellerstedt operator in principal part

A. H. Attaev

Institution of Applied Mathematics and Automation, Nal'chik, 360000, Russian Federation

Abstract: In the paper we study a loaded degenerate hyperbolic equation of the second order with variable coefficients. The principal part of the equation is the Gellerstedt operator. The loaded term is given in the form of the trace of desired solution on the degenerate line. The latter is located in the inner part of the domain. We investigate a boundary value problem. The boundary conditions are given on a characteristics line of the equation under study. For the model equation (when all subordinated coefficients are zero) we construct an explicit representation for solution of the Goursat problem. In the general case, we reduce the problem to an integral Volterra equation of the second kind. We apply the method realized by Sven Gellerstedt solving the second Darboux problem. In both cases, model and general, we use widely properties of the Green–Hadamard function.

Keywords: Goursat problem, loaded equation, hyperbolic equation, degenerate equation, Gellerstedt operator, the Green–Hadamard's function method

DOI: https://doi.org/10.14498/vsgtu1452

Full text: PDF file (681 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 517.956.3
MSC: 35L80
Original article submitted 13/X/2015
revision submitted – 23/X/2015

Citation: A. H. Attaev, “Goursat problem for loaded degenerate second order hyperbolic equation with Gellerstedt operator in principal part”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 20:1 (2016), 7–21

Citation in format AMSBIB
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\by A.~H.~Attaev
\paper Goursat problem for loaded degenerate second order hyperbolic equation with Gellerstedt operator in principal part
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2016
\vol 20
\issue 1
\pages 7--21
\mathnet{http://mi.mathnet.ru/vsgtu1452}
\crossref{https://doi.org/10.14498/vsgtu1452}
\zmath{https://zbmath.org/?q=an:06964468}
\elib{https://elibrary.ru/item.asp?id=26898032}


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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. K. U. Khubiev, “Zadachi so smescheniem dlya nagruzhennogo uravneniya giperbolo-parabolicheskogo tipa s operatorom drobnoi diffuzii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:1 (2018), 82–90  mathnet  crossref  elib
    2. A. Kh. Attaev, “Kharakteristicheskaya zadacha dlya nagruzhennogo vdol odnoi iz svoikh kharakteristik giperbolicheskogo uravneniya vtorogo poryadka”, Vestnik KRAUNTs. Fiz.-mat. nauki, 2018, no. 3(23), 14–18  mathnet  crossref  elib
    3. A. Kh. Attaev, “Characteristic problems for a loaded equation of hyperbolic type with a wave operator in the principal part”, International Conference on Analysis and Applied Mathematics (ICAAM 2018), AIP Conf. Proc., 1997, eds. A. Ashyralyev, A. Lukashov, M. Sadybekov, Amer. Inst. Phys., 2018, UNSP 020022-1  crossref  isi  scopus
    4. K. U. Khubiev, “Kraevaya zadacha dlya nagruzhennogo uravneniya giperbolo-parabolicheskogo tipa s vyrozhdeniem poryadka v oblasti ego giperbolichnosti”, Materialy mezhdunarodnoi nauchnoi konferentsii «Aktualnye problemy prikladnoi matematiki i fiziki» Kabardino-Balkariya, Nalchik, 17–21 maya 2017 g., Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 149, VINITI RAN, M., 2018, 113–117  mathnet  mathscinet
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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