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 Trudy Inst. Mat. i Mekh. UrO RAN, 2010, Volume 16, Number 2, Pages 91–108 (Mi timm551)

Application of the generalized method of characteristic series to the construction of a solution of an initial-boundary value problem for a system of quasi-linear equations

A. L. Kazakov

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences

Abstract: A generalization of the method of characteristic series developed by A. F. Sidorov is suggested. The method is applied to the investigation of initial-boundary value problems for partial differential equations, including equations appearing in gas dynamics. A solution of a mixed problem for a system of quasi-linear equations is constructed in the form of multiple series in powers of characteristic functions, and the corresponding analog of the Cauchy–Kovalevskaya theorem is proved.

Keywords: partial differential equations, initial-boundary value problem, series, gas dynamics.

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Citation: A. L. Kazakov, “Application of the generalized method of characteristic series to the construction of a solution of an initial-boundary value problem for a system of quasi-linear equations”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 2, 2010, 91–108

Citation in format AMSBIB
\Bibitem{Kaz10} \by A.~L.~Kazakov \paper Application of the generalized method of characteristic series to the construction of a~solution of an initial-boundary value problem for a~system of quasi-linear equations \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2010 \vol 16 \issue 2 \pages 91--108 \mathnet{http://mi.mathnet.ru/timm551} \elib{http://elibrary.ru/item.asp?id=14809442} 

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Erratum

This publication is cited in the following articles:
1. Kazakov A.L., Dronova A.V., “Primenenie obobschennogo metoda kharakteristicheskikh ryadov dlya postroeniya kusochno-analiticheskikh reshenii uravnenii s chastnymi proizvodnymi”, Vestn. Uralskogo gos. un-ta putei soobscheniya, 2010, no. 3, 46–55
2. A. L. Kazakov, “Primenenie kharakteristicheskikh ryadov dlya postroeniya reshenii nelineinykh parabolicheskikh uravnenii i sistem s vyrozhdeniem”, Tr. IMM UrO RAN, 18, no. 2, 2012, 114–122
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