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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2016, Volume 20, Number 1, Pages 7–21
DOI: https://doi.org/10.14498/vsgtu1452
(Mi vsgtu1452)
 

This article is cited in 5 scientific papers (total in 5 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
Full-text PDF (681 kB) Citations (5)
(published under the terms of the Creative Commons Attribution 4.0 International License)
References:
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.
Original article submitted 13/X/2015
revision submitted – 23/X/2015
Bibliographic databases:
Document Type: Article
UDC: 517.956.3
MSC: 35L80
Language: Russian
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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  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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