References
Lax, P. D., Hyperbolic systems of conservation laws, II. Comm. Pure Appl. Math. 10, 537–566 (1957).
Courant, R., & K. O. Friedrichs, Supersonic Flows and Shock Waves. New York:Interscience 1948.
Johnson, J. L., & J. A. Smoller, Global solutions for certain systems of quasi-linear hyperbolic conservation laws. J. Math. Mech. 17, 561–576 (1967).
Greenberg, J. M., On the interactions of shocks and simple waves of the same family. Arch. Rational Mech. Anal. 37, 136–160 (1970).
Moler, C., & J. A. Smoller, Elementary interactions in quasi-linear hyperbolic systems. Arch. Rational Mech. Anal. 37, 309–322 (1970).
Glimm, J., Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math. 18, 697–715 (1965).
Glimm, J., & P. D. Lax, Decay of solutions of systems of hyperbolic conservation laws. N.Y.U.A.E.C. report, N.Y. O-1480-115, April, 1969.
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Communicated by M. E. Gurtin
This research was supported by the National Science Foundation, Grant No. GP 2289.
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Greenberg, J. On the elementary interactions for the quasilinear wave equation \(\frac{{\partial \gamma }}{{\partial t}} - \frac{{\partial v}}{{\partial x}} = 0\) and\(\frac{{\partial v}}{{\partial t}} - \frac{{\partial \sigma \left( \gamma \right)}}{{\partial x}} = 0\) . Arch. Rational Mech. Anal. 43, 325–349 (1971). https://doi.org/10.1007/BF00252000
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DOI: https://doi.org/10.1007/BF00252000