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The existence and uniqueness of self-similar solutions involving Jouguet points on the shock adiabatic curve. (English. Russian original) Zbl 0893.76093
J. Appl. Math. Mech. 60, No. 1, 61-65 (1996); translation from Prikl. Mat. Mekh. 60, No. 1, 66-71 (1996).
The authors study self-similar solutions for hyperbolic system of one-dimensional conservation laws, and explain such phenomena as nonuniqueness and the absence of continuous dependence of solutions on parameters by the presence of a “foreign” Jouguet point on the shock adiabat.
MSC:
76V05 Reaction effects in flows
76L05 Shock waves and blast waves in fluid mechanics
80A25 Combustion
35L65 Hyperbolic conservation laws
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[1] Kulikovskii, A.G.; Sveshnikova, Ye.I., The self-similar problem of the action of an abrupt load on the boundary of an elastic half-space, Prikl. mat. mekh., 49, 2, 284-291, (1985)
[2] Kulikovskii, A.G.; Sveshnikova, Ye.L., The decomposition of an arbitrary shock wave in an elastic medium, Prikl. mat. mekh., 52, 6, 1001-1007, (1988)
[3] Kulikovskii, A.G., Special features in the behaviour of non-linear quasitransverse waves in a weakly anisotropic elastic medium, Trudy mat. inst. im. V.A. steklova, akad, nauk SSSR, 186, 132-139, (1989)
[4] Kulikovskii, A.G.; Sveshnikova, Ye.I., Some properties of the shock adiabat of quasitransverse elastic waves, Prikl. mat. mekh., 48, 5, 793-798, (1984) · Zbl 0585.73023
[5] LAX P., Hyperbolic systems of conservation laws II Comm. Pure and Appl. Math.{\bf10}, 4, 537-566. · Zbl 0081.08803
[6] Landau, L.D.; Lifshits, Ye.M., Hydrodynamics, (1986), Nauka Moscow
[7] Kulikovskii, A.G.; Sveshnikova, Ye.I., Investigation of the shock adiabat of quasitransverse shock waves in a prestressed medium, Prikl. mat. mekh., 46, 5, 831-840, (1982)
[8] Kulikovskii, A.G.; Sveshnikova, Ye.I., Equations describing the propagation of quasitransverse waves in a weakly anisotropic medium, Prikl. mat. mekh., 50, 4, 597-604, (1986)
[9] Hanyga, A., On the solution to the Riemann problem for arbitrary hyperbolic system of conservation laws, Publ. inst. Pol. ac. sci., No. A-1(98), 1-123, (1976)
[10] Kulikovskii, A.G., Properties of shock adiabatic curves in the neighbourhood of jouguet points, Izv. akad. nauk SSSR, mzhg, 2, 184-186, (1979)
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