Geodesic
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 Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 2, pp. 91-108

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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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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 Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 2, pp. 91-108. http://geodesic.mathdoc.fr/item/TIMM_2010_16_2_a6/