A system of non-strictly hyperbolic conservation laws arising in elasticity theory. (English) Zbl 0434.73019


74M20 Impact in solid mechanics
74B99 Elastic materials
74H99 Dynamical problems in solid mechanics
35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations


Riemann problem
Full Text: DOI


[1] Borovikov, V. A., On the decomposition of a discontinuity for a system of two quasilinear equations. Transactions Moscow Math Soc. Vol. 27, 53-94. · Zbl 0296.35052
[2] Carrier, G. F., On the non-linear vibration problem of the elastic string. Quart. Appl. Math. 3 (1945) 157-165. · Zbl 0063.00715
[3] Courant, R., & K. O. Friedrichs, Supersonic Flow and Shock Waves. Interscience, 1948. · Zbl 0041.11302
[4] Conley, C. C, & J. A. Smoller, Viscosity matrices for two-dimensional nonlinear hyperbolic systems. Comm. Pure Appl. Math. 23 (1970) 867-84. · Zbl 0204.11303
[5] Cristescu, N., Dynamic Plasticity, North-Holland, 1967. · Zbl 0158.43604
[6] Glimm, J., Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math. 18 (1965), 697-715. · Zbl 0141.28902
[7] Iosue, R.V., A Case Study of Shocks in Non-linear Elasticity. Ph.D. Thesis, Adelphi University, 1971.
[8] Keyfitz, B. L., & H. C. Kranzer, Existence and uniqueness of entropy solutions to the Riemann problem for hyperbolic systems of two non-linear conservation laws. Jour. Diff. E., 27 (1978), 444-475. · Zbl 0364.35036
[9] Keyfitz, B. L., & H. C. Kranzer, The Riemann problem for some non-strictly hyperbolic systems of conservation laws. Notices A.M.S. 23 (1976), A-127-128.
[10] Korchinski, D. J. Solution of a Riemann problem for a 2 x 2 system of conservation laws possessing no classical weak solution. Ph.D. Thesis, Adelphi University, 1977.
[11] Lax, P. D., Hyperbolic systems of conservation laws II. Comm. Pure Appl. Math. 10 (1957) 537-566. · Zbl 0081.08803
[12] Lax, P. D., Shock Waves and Entropy, in Contributions to Nonlinear Functional Analysis, ed. E. H. Zarantonello, Academic Press, 1971. · Zbl 0268.35014
[13] Liu, T. P. The Riemann Problem for General 2 x 2 Conservation Laws. Trans. Amer. Math. Soc. 199 (1974), 89-112. · Zbl 0289.35063
[14] Smoller, J. A., & J. L. Johnson. Global solutions for an extended class of hyperbolic systems of conservation laws. Arch. Rational Mech. Anal. 32 (1969) 169-189. · Zbl 0167.10204
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