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Systems of conservation laws of mixed type. (English) Zbl 0413.34017

MSC:
34A99 General theory for ordinary differential equations
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[1] Bers, L, Mathematical aspects of subsonic and transonic gas dynamics, (1958), Wiley New York · Zbl 0083.20501
[2] Bristeau, M, Application of optimal control and finite element methods to the calculation of transonic flows and incompressible flows, IRIA research report 294, (April 1978)
[3] Conley, C.C; Smoller, J.A; Conley, C.C; Smoller, J.A; Conley, C.C; Smoller, J.A, Shock waves as progressive wave solutions of higher order equations, Comm. pure appl. math., Comm. pure appl. math., Comm. pure appl. math., 25, 133-146, (1972) · Zbl 0225.35067
[4] D’Yachenko, V.F, Cauchy problem for quasilinear equations, Dokl. akad. nauk SSSR, 136, 16-17, (1961)
[5] Friedrichs, K.O; Lax, P.D, Systems of conservation laws with a convex extention, (), 1686-1688 · Zbl 0229.35061
[6] Gel’fand, I.M, Some problems in the theory of quasilinear equations, Amer. math. soc. transl. sect., 2, No. 29, 295-381, (1963) · Zbl 0127.04901
[7] Glimm, J, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. pure appl. math., 18, 697-715, (1965) · Zbl 0141.28902
[8] Godunov, S.K, An interesting class of quasilinear systems, Dokl. akad. nauk SSSR, 139, 521-523, (1961) · Zbl 0125.06002
[9] Hopf, E, On the right weak solution of the Cauchy problem for quasilinear equations of the first order, J. math. mech., 19, 483-487, (1969) · Zbl 0188.16102
[10] Jameson, A, Numerical solutions of partial differential equations of mixed type, ()
[11] {\scB. L. Keyfitz and H. C. Kranzer}, A system of non-strictly hyperbolic conservation laws arising in elasticity theory, Arch. Rational Mech. Anal., in press. · Zbl 0434.73019
[12] Keyfitz, B.L; Kranzer, H.C, Existence and uniqueness of entropy solutions to the Riemann problem for hyperbolic systems of two nonlinear systems of conservation laws, J. differential equations, 27, 444-476, (1978) · Zbl 0364.35036
[13] Lax, P.D, Hyperbolic systems of conservation laws, II, Comm. pure appl. math., 10, 537-566, (1957) · Zbl 0081.08803
[14] Lax, P.D, Shock waves and entropy, (), 603-634
[15] Mock, M.S, On fourth-order dissipation and single conservation laws, Comm. pure appl. math., 29, 383-388, (1976) · Zbl 0327.76031
[16] Mock, M.S, Discrete shocks and genuine nonlinearity, Michigan math. J., 25, 131-146, (1978) · Zbl 0397.35044
[17] Mock, M.S, A difference scheme employing fourth-order “viscosity” to enforce an entropy inequality, () · Zbl 0377.65049
[18] Morawetz, C.S; Morawetz, C.S; Morawetz, C.S, On the non-existence of continuous transonic flows past profiles, I-III, Comm. pure appl. math., Comm. pure appl. math., Comm. pure appl. math., 11, 129-144, (1958) · Zbl 0139.44003
[19] {\scC. S. Morawetz}, A regularization for a simple model of transonic flow, to be published. · Zbl 0448.35067
[20] Murman, E.M; Cole, J.D, Calculation of plane steady transonic flows, Aiaa j., 9, 114-121, (1971) · Zbl 0249.76033
[21] Oleinik, O.A, On the uniqueness of the generalized solution of the Cauchy problem for a nonlinear system occurring in mechanics, Uspechi mat. nauk, 12, 169-176, (1957) · Zbl 0080.07702
[22] Vvedenskaya, N.D, An instance of nonuniqueness of the generalized solutions to a quasilinear system of equations, Dokl. akad. nauk SSSR, 136, 532-533, (1961)
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