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Vladikavkaz. Mat. Zh., 2016, Volume 18, Number 2, Pages 19–30 (Mi vmj577)  

This article is cited in 2 scientific papers (total in 2 papers)

The first boundary value problem for a degenerate hyperbolic equation

Zh. A. Balkizov

Institute of Applied Mathematics and Automation, Nalchik, Russia

Abstract: Under certain hypothesis on the coefficients the condition is found for unique solvability of the first boundary value problem for a degenerate hyperbolic equation in the region. The uniqueness of the solution of the problem is proved by Tricomi method and existence by the method of integral equations. The solutions obtained with respect to the traces of the sought solution of integral equations are found and written out explicitly. It is shown that whenever the hypothesis of the theorem is violated, then the homogeneous problem corresponding to the problem under study has an infinite number of linearly independent solutions.

Key words: degenerate hyperbolic equation, first boundary value problem, Goursat problem, Cauchy problem, Mittag-Leffler function.

Full text: PDF file (229 kB)
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UDC: 517.95
Received: 30.06.2015

Citation: Zh. A. Balkizov, “The first boundary value problem for a degenerate hyperbolic equation”, Vladikavkaz. Mat. Zh., 18:2 (2016), 19–30

Citation in format AMSBIB
\Bibitem{Bal16}
\by Zh.~A.~Balkizov
\paper The first boundary value problem for a~degenerate hyperbolic equation
\jour Vladikavkaz. Mat. Zh.
\yr 2016
\vol 18
\issue 2
\pages 19--30
\mathnet{http://mi.mathnet.ru/vmj577}


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    This publication is cited in the following articles:
    1. R. Kh. Makaova, “Kraevaya zadacha dlya giperbolicheskogo uravneniya tretego poryadka s vyrozhdeniem poryadka vnutri oblasti”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 21:4 (2017), 651–664  mathnet  crossref  zmath  elib
    2. R. Kh. Makaova, “Zadacha Trikomi dlya vyrozhdayuschegosya vnutri oblasti giperbolicheskogo uravneniya tretego poryadka”, Vestnik KRAUNTs. Fiz.-mat. nauki, 2018, no. 3(23), 67–75  mathnet  crossref  elib
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