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Solution of the Riemann problem for a class of hyperbolic systems of conservation laws by the viscosity method. (English) Zbl 0262.35034


MSC:

35L45 Initial value problems for first-order hyperbolic systems
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[1] Riemann, B., Über die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite. Gesammelte Mathematische Werke (H. Weber, ed.), pp. 145–164. Leipzig: B. G. Teubner 1876
[2] Glimm, J., Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math. 18, 697–715 (1965) · Zbl 0141.28902 · doi:10.1002/cpa.3160180408
[3] Lax, P. D., Hyperbolic systems of conservation laws II. Comm. Pure Appl. Math. 10, 537–556 (1957) · Zbl 0081.08803 · doi:10.1002/cpa.3160100406
[4] Smoller, J. A., On the solution of the Riemann problem with general step data for an extended class of hyperbolic systems. Mich. Math. J. 16, 201–210 (1969) · Zbl 0185.34501 · doi:10.1307/mmj/1029000262
[5] Wendroff, B., The Riemann problem for materials with nonconvex equation of state. Part I: Isentropic flow. J. Math. Anal. Appl. 38, 454–466 (1972) · Zbl 0264.76054 · doi:10.1016/0022-247X(72)90103-5
[6] gemLeibovich, L., Solutions of the Riemann problem for hyperbolic systems of quasilinear equations without convexity conditions. J. Math. Anal. Appl. (to appear).
[7] Conley, C. C., & J. A. Smoller, Viscosity matrices for two-dimensional nonlinear hyperbolic systems. Comm. Pure Appl. Math. 23, 867–884 (1970) · Zbl 0201.43301 · doi:10.1002/cpa.3160230603
[8] Lax, P. D., A concept of entropy. Contributions to Nonlinear Functional Analysis (E. H. Zarantonello, ed.), pp. 603–634. New York: Academic Press 1971
[9] gemDafermos, C. M., The entropy rate admissibility criterion for solutions of hyperbolic conservation laws. J. Diff. Equations 14 (1973)
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