References
Courant, R., & K. O. Friedrichs, Supersonic Flow and Shock Waves. New York: Interscience 1948.
Glimm, J., Solutions in the large for nonlinear hyperbolic sytems of equations. Comm. Pure Appl. Math. 18, 695–717 (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.
Johnson, J. L., Global continuous solutions of hyperbolic systems of quasi-linear equations. Bull. A.M.S. 73, 639–641 (1967).
Johnson, J. L., & J. A. Smoller, Global solutions of hyperbolic systems of conservation laws in two dependent variables. Bull. A.M.S. 74, 915–918 (1968).
Nishida, T., Global solution for an initial boundary value problem of a quasilinear hyperbolic system. Proc. Jap. Acad., 44, 642–646 (1968).
Smoller, J. A., On the solution of the Riemann problem with general step data for an extended class of hyperbolic system. Mich. Math. J. 16, 201–210 (1969).
Smoller, J. A., & J. L. Johnson, Global solutions for an extended class of hyperbolic systems of conservation laws. Arch. Rational Mech. Anal. 32, 169–189 (1969).
Yamaguti, M., & T. Nishida, On some global solution for quasi-linear hyperbolic equations. Funk. Ekv. 11, 51–57 (1968).
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Communicated by L. Cesari
C. Moler was supported in part by the Office of Naval Research, Contract NR 044-377, and J. Smoller by the Air Force Office of Scientific Research, Contract AFOSR-69-1662.
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Moler, C., Smoller, J. Elementary interactions in quasi-linear hyperbolic systems. Arch. Rational Mech. Anal. 37, 309–322 (1970). https://doi.org/10.1007/BF00251610
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DOI: https://doi.org/10.1007/BF00251610