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/

[1] Kupant R., Uravneniya s chastnymi proizvodnymi, Mip, M., 1964, 830 pp. | MR

[2] Sidopov A. F., “Metod resheniya nekotorykh kraevykh zadach dlya nelineinykh uravnenii giperbolicheskogo tipa i rasprostranenie slabykh udarnykh voln”, Ppikl. matematika i mekhanika, 36:3 (1972), 426–434

[3] Sidorov A. F., “Application of characteristic series to the solution of three-dimensional problems in gas dynamics”, Numerical methods in fluid dynamics, Mir, M., 1984, 184–206 | MR

[4] Titov S. S., “Razlozhenie reshenii nelineinykh uravnenii v dvoinye ryady”, Differents. uravneniya, 14:10 (1978), 1844–1850 | MR | Zbl

[5] Titov S. S., “Ob analitichnosti reshenii uravneniya Kortevega-de Friza, predstavlennykh ryadami eksponent”, Differents. uravneniya, 25:2 (1989), 343–350 | MR

[6] Filimonov M. Yu., Korzunin L. G., Sidorov A. F., “Approximate methods for solving nonlinear initial boundary-value problems based on special constructions of series”, Russian J. Numer. Anal. Math. Modelling, 8:2 (1993), 101–125 | DOI | MR | Zbl

[7] Bautin S. P., “Kharakteristicheskaya zadacha Koshi dlya kvazilineinoi analiticheskoi sistemy”, Differents. uravneniya, 12:11 (1976), 2052–2063 | MR | Zbl

[8] Sidorov A. F., Izbrannye trudy: Matematika. Mekhanika, Fizmatlit, M., 2001, 576 pp. | MR

[9] Ovsyannikov L. V., Lektsii po osnovam gazovoi dinamiki, Institut kompyuternykh issledovanii, M.–Izhevsk, 2003, 336 pp.