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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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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2014, Issue 1(34), Pages 37–47
DOI: https://doi.org/10.14498/vsgtu1280 (Mi vsgtu1280) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Differential Equations

A Boundary-value Problem with Shift for a Hyperbolic Equation Degenerate in the Interior of a Region

O. A. Repinab, S. K. Kumykovac

a Samara State Technical University, Samara, 443100, Russian Federation
b Samara State Academy of Economics, Samara, 443090, Russian Federation
c Kabardino-Balkar State University, Nalchik, 360004, Russian Federation
Full-text PDF (617 kB) Citations (4)
(published under the terms of the Creative Commons Attribution 4.0 International License)
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DOI: https://doi.org/10.14498/vsgtu1280
Abstract: For a degenerate hyperbolic equation in characteristic region (lune) a boundary-value problem with operators of fractional integro-differentiation is studied. The solution of this equation on the characteristics is related point-to-point to the solution and its derivative on the degeneration line. The uniqueness theorem is proved by the modified Tricomi method with inequality-type constraints on the known functions. Question of the problem solution’s existence is reduced to the solvability of a singular integral equation with Cauchy kernel of the normal type.
Keywords: Cauchy problem, boundary-value problem with shift, fractional integro-differentiation operators, singular equation with Cauchy kernel, regularizer, Gauss hypergeometric function, Euler gamma function.
Original article submitted 04/XII/2013
revision submitted – 11/II/2014
Bibliographic databases:
Document Type: Article
UDC: 517.956.326
MSC: Primary 35L80; Secondary 35L20, 35C15
Language: Russian
Citation: O. A. Repin, S. K. Kumykova, “A Boundary-value Problem with Shift for a Hyperbolic Equation Degenerate in the Interior of a Region”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(34) (2014), 37–47
Citation in format AMSBIB
\Bibitem{RepKum14}
\by O.~A.~Repin, S.~K.~Kumykova
\paper A~Boundary-value Problem with Shift for a~Hyperbolic Equation Degenerate in the Interior of a~Region
\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 37--47
\mathnet{http://mi.mathnet.ru/vsgtu1280}
\crossref{https://doi.org/10.14498/vsgtu1280}
\zmath{https://zbmath.org/?q=an:06968823}
\elib{https://elibrary.ru/item.asp?id=22813958}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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