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The application of the differential-constraints method to the two-dimensional equations of gas dynamics. (English. Russian original) Zbl 1049.76581

J. Appl. Math. Mech. 63, No. 6, 885-891 (1999); translation from Prikl. Mat. Mekh. 63, No. 6, 947-954 (1999).
The authors discuss new application of the method of differential constraints (see [ A. F. Sidorov, V. P. Shapeev and N. N. Janenko, “Method of differential constraints and its applications in gas dynamics”, Novosibirsk, Nauka (1984; Zbl 0604.76062)] ). The object of application is the two-dimensional equations of gas dynamics with plane and axis symmetry. The classification of the obtained solutions is presented. No numerical results are cited.

MSC:

76N15 Gas dynamics (general theory)
76M99 Basic methods in fluid mechanics

Citations:

Zbl 0604.76062

Software:

REDUCE
PDFBibTeX XMLCite

References:

[1] Yanenko, N. N.: The theory of compatibility and methods of integrating systems of non-linear partial differential equations. Proceedings of the fourth all-union mathematical conference 2, 613-621 (1964)
[2] Sidorov, A. F.; Shapeev, V. P.; Yanenko, N. N.: The method of differential constraints and its applications in gas dynamics. (1984) · Zbl 0604.76062
[3] Cartan, E.: LES systèmes différentiels extérieurs et leurs applications geometriques. 215 (1945)
[4] Finikov, S. P.: The Cartan method of exterior forms in differential geometry. (1948) · Zbl 0033.06004
[5] Kuranishi, M.: Lectures on involutive systems of partial differential equations. 77 (1967) · Zbl 0163.12001
[6] Meyer, R. E.: On waves of finite amplitude in ducts. I. wave fronts. II. waves of moderate amplitude. Q.J. mech. Appl. math. 5, No. 3, 257-291 (1952) · Zbl 0047.18503
[7] Mises, R.: Mathematical theory of compressible fluid flow. 514 (1958) · Zbl 0083.20403
[8] Sedov, L. I.: Two-dimensional problems in hydro- and aerodynamics. (1965) · Zbl 0131.40901
[9] Shurygin, V. A.; Yanenko, N. N.: The realization of algebraic differential algorithms on electronic computers. Problems of cybernetics 6 (1961) · Zbl 0171.38203
[10] Arais, Ye.A.; Shapeev, V. P.; Yanenko, N. N.: The realization of the Cartan method of exterior forms on a computer. Dokl. akad. Nauk SSSR 214, No. 4, 737-738 (1974)
[11] Ganzha, V. G.; Meleshko, S. V.; Shapeev, V. P.: Automation of compatibility analysis of quasilinear PDE systems with the aid of the REDUCE system. Computer algebra and its applications to mechanics, 89-96 (1993)
[12] Hearn, A. C.: REDUCE user’s manual. 53 (1967)
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