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Homogeneous autonomous systems with three independent variables. (English. Russian original) Zbl 0923.76272
Summary: Double-wave solutions of equations with three independent variables are studied. The case when a homogeneous autonomous system consisting of four independent quasilinear first-order differential equations can be formed to study compatibility, is considered. All such systems having solutions with an arbitrary function that cannot be reduced to invariant ones are given, and their solutions are found.

MSC:
76N15Gas dynamics, general
35Q35PDEs in connection with fluid mechanics
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References:
[1] Ovsyannikov, L. V.: Group analysis of differential equations. (1978) · Zbl 0484.58001
[2] Sidorov, A. F.; Shapeyev, V. P.; Yanenko, N. N.: The method of differential connections and its applications in gas dynamics. (1984)
[3] Pogodin, Yu.Ya.; Suchkov, V. A.; Yanenko, N. N.: Travelling waves in the equations of gas dynamics. Dokl. akad. Nauk SSSR 119, No. 3, 443-445 (1958) · Zbl 0122.43801
[4] Sidorov, A. F.; Yanenko, N. N.: The problem of the unsteady planar flows of a polytropic gas with rectilinear characteristics. Dokl. akad. Nauk SSSR 123, No. 5, 832-834 (1958)
[5] Kucharaczyk, P.; Peradzynski, Z.; Zawistowska, E.: Unsteady multidimensional isentropic flows described by linear Riemann invariants. Arch. mech. 25, No. 2, 319-350 (1973) · Zbl 0267.35008
[6] Peradzynski, Z.: Hyperbolic flows in ideal plasticity. Arch. mech. 27, No. 1, 141-156 (1975) · Zbl 0322.73019
[7] Meleshko, S. V.: The classification of planar isentropic gas flows of double wave type. Prikl. mat. Mekh. 49, No. 3, 406-410 (1985)
[8] Meleshko, S. V.: Non-isentropic three-dimensional steady and planar unsteady waves. Prikl. mat. Mekh. 53, No. 2, 255-260 (1989)
[9] Meleshko, S. V.: Double waves in an ideal rigid-plastic body under planar deformation. Prikl. mekh. Tekh fiz. 2, 131-136 (1990)
[10] Meleshko, S. V.: The solutions with degenerate hodograph of quasistationary equations of the theory of plasticity under Mises fluidity condition. Prikl. mekh. Tekh. fiz. 1, 82-88 (1991)
[11] Smirnov, V. I.: Advanced mathematics. 4 (1951) · Zbl 0044.32002