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On the structure of quasitransverse elastic shock waves. (English. Russian original) Zbl 0678.73020
J. Appl. Math. Mech. 51, No. 6, 711-716 (1987); translation from Prikl. Mat. Mekh. 51, No. 6, 926-932 (1987).
Summary: The structure of quasitransverse shock waves in a slightly anisotropic medium in the presence of dissipation due to viscosity is investigated. The existence of a shock structure “responsible” for ambiguity of the solution of a selfsimilar problem about waves excited in a half-space is demonstrated. The question of the existence of a structure for the remaining quasitransverse shock waves is discussed.

MSC:
74M20 Impact in solid mechanics
76L05 Shock waves and blast waves in fluid mechanics
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[1] Galin, G.Ya., On the theory of shock waves, Dokl. akad. nauk SSSR, 127, 1, (1959) · Zbl 0353.76044
[2] Oleinik, O.A., On the uniqueness and stability of a generalized solution of the Cauchy problem for a quasilinear equation, Usp. matem. nauk, 14, 2, (1959) · Zbl 0087.30401
[3] Kalashnikov, A.S., Construction of generalized solutions of quasilinear first-order equations without a convexity condition as the limits of solutions of parabolic equations with a small parameter, Dokl. akad. nauk SSSR, 127, 1, (1959) · Zbl 0100.09203
[4] Kulikovskii, A.G., On the possible influence of oscillations in the structure of a discontinuity in a set of allowable discontinuities, Dokl. akad. nauk SSSR, 275, 6, (1984)
[5] Rozhdestvenskii, B.L.; Yanenko, N.N., Systems of quasilinear equations and their application to gas dynamics, (1978), Nauka Moscow · Zbl 0177.14001
[6] Kulikovskii, A.G.; Sveshnikova, E.I., The selfsimilar problem of the action of a sudden load on the boundary of an elastic half-space, Pmm, 49, 2, (1985) · Zbl 0603.73019
[7] Kulikovskii, A.G.; Sveshnikova, E.I., Non-linear waves occurring during stress changes on the boundary of an elastic half-space, problems of the non-linear mechanics of a continuous medium, (1985), Valgus Tallin
[8] Kulikovskii, A.G.; Sveshnikova, E.I., On shock waves propagating over the state of stress in isotropic non-linearly elastic media, Pmm, 44, 3, (1980)
[9] Kulikovskii, A.G.; Sveshnikova, E.I., Investigation of the shock adiabatic of quasitransverse shock waves in a prestressed elastic medium, Pmm, 46, 5, (1982) · Zbl 0542.73024
[10] Bland, D.R., Non-linear dynamical elasticity theory, (1972), Mir Moscow · Zbl 0242.73002
[11] Kulikovskii, A.G., On equations describing quasitransverse wave propagation in a slightly non-isotropic elastic body, Pmm, 50, 4, (1986)
[12] Sveshnikova, E.I., Simple waves in a non-linearly elastic medium, Pmm, 46, 4, (1982)
[13] Godunov, S.K., On the concept of a generalized solution, Dokl. akad. nauk SSSR, 134, 6, (1960) · Zbl 0104.31901
[14] Godunov, S.K., On the non-unique smoothing of discontinuities in solutions of quasilinear systems, Dokl. akad. nauk SSSR, 136, 2, (1961) · Zbl 0117.06401
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