DiPerna, Ronald J. Decay of solutions of hyperbolic systems of conservation laws with a convex extension. (English) Zbl 0348.35071 Arch. Ration. Mech. Anal. 64, 1-46 (1977). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 11 Documents MSC: 35L65 Hyperbolic conservation laws 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs PDFBibTeX XMLCite \textit{R. J. DiPerna}, Arch. Ration. Mech. Anal. 64, 1--46 (1977; Zbl 0348.35071) Full Text: DOI References: [1] Bakhrarov, N., On the existence of regular solutions in the large for quasilinear hyperbolic systems, Zhur. Vychisl. Mat. i Mathemat. Fiz., 10, 969-980 (1970). [2] Courant, R. & K.O. Friedrichs, ?Supersonic Flow and Shock Waves?, New York: Interscience Publishers, Inc., 1948. · Zbl 0041.11302 [3] Dafermos, C.M., private communications. [4] Dafermos, C.M., The entropy rate admissibility criterion for solutions of hyperbolic conservation laws, J. Differential Eq., 14, 202-212 (1973). · Zbl 0262.35038 [5] DiPerna, R.J., Global solutions to a class of nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math., 26, 1-28 (1973). · Zbl 0256.35053 [6] Federer, H., ?Geometric Measure Theory.? New York: Springer 1969. · Zbl 0176.00801 [7] Friedrichs, K.O., On the laws of relativisitc electro-magneto-fluid dynamics, Comm. Pure Appl. Math., 27, 749-808 (1974). · Zbl 0308.76075 [8] Friedrichs, K.O. & P.D. Lax, Systems of conservation laws with a convex extension, Proc. Nat. Acad. Sci. USA 68, 1686-1688 (1971). · Zbl 0229.35061 [9] Glimm, J., Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 18, 697-715 (1965). · Zbl 0141.28902 [10] Glimm, J. & P.D. Lax, Decay of solutions of systems of nonlinear hyperbolic conservation laws, Amer. Math. Soc., 101 (1970). · Zbl 0204.11304 [11] Gogosov, V.V., Resolution of an arbitrary discontinuity in magnetohydrodynamics, J. Appl. Math. Mech., 25, 148-197 (1961). [12] Greenberg, J.M., Estimates for fully developed shock solutions to the equation ?u/?t-?v/?x=0 and ?v/?t-??(u)/x, Indiana Univ. Math. J., 22, 989-1003 (1973). · Zbl 0259.35051 [13] Greenberg, J.M., Decay theorems for stopping shock problems, preprint. · Zbl 0311.35069 [14] Jeffrey, A. & T. Taniuti Non-linear Wave Propagation with Applications to Physics and Magnetohydrodynamics. New York: Academic Press 1964. · Zbl 0117.21103 [15] John, F., Formation of singularities in one-dimensional nonlinear wave propagation, Comm. Pure Appl. Math., 27, 377-405 (1974) · Zbl 0302.35064 [16] Kuznetsov, N.N. & V.A. Tupshiev, A certain generalization of a theorem of Glimm, Dokl. Akad. Nauk. SSSR, 221, 287-290 (1975). [17] Lax, P.D., Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math., 10, 537-566 (1957). · Zbl 0081.08803 [18] Lax, P.D., Shock waves and entropy, ?Contributions to Nonlinear Functional Analysis?, ed. E.A. Zarantonello, 603-634. New York: Academic Press 1971. [19] Lax, P.D., The formation and decay of shock waves, Amer. Math. Monthly, 79, 227-241 (1972). · Zbl 0228.35019 [20] Liu, T. P., Solutions in the large for the nonisentropic equations of gas dynamics, preprint. · Zbl 0361.35056 [21] Nishida, T., Global solutions for an initial boundary value problem of a quasilinear hyperbolic system, Proc. Japan Acad., 44, 642-646 (1968) · Zbl 0167.10301 [22] Nishida, T. & J.A. Smoller, Solutions in the large for some nonlinear hyperbolic conservation laws, Comm. Pure Appl. Math, 26, 183-200 (1973). · Zbl 0267.35058 [23] 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 [24] Smoller, J.A. & J.L. Jonson, Global solutions for an extended class of hyperbolic systems of conservation laws. Arch. Rational Mech. Anal., 37, pp. 399-400 (1970). · Zbl 0197.07701 [25] Taub, A.H., Relativistic Rankine-Hugoniot equations, Phys. Rev., 74, 328-334 (1948). · Zbl 0035.12103 [26] Vol’pert, A.I., the spaces BV and quasilinear equations, Math. USSR Sb., 2, 257-267 (1967). · Zbl 0168.07402 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.