Singularities of solutions of nonlinear hyperbolic systems of conservation laws. (English) Zbl 0324.35062


35L60 First-order nonlinear hyperbolic equations
35L65 Hyperbolic conservation laws
Full Text: DOI


[1] Federer, H., Geometric Measure Theory. New York: Springer 1969. · Zbl 0176.00801
[2] Glimm, J., Solutions in the large for nonlinear hyperbolic systems of conservation laws. Comm. Pure Appl. Math. 18, 697–715 (1965). · Zbl 0141.28902
[3] Glimm, J., & P.D. Lax, Decay of solutions of nonlinear hyperbolic conservation laws. Mem. Amer. Math. Soc. 101 (1970). · Zbl 0204.11304
[4] Golubitsky, M, & D.G. Schaeffer, Stability of shock waves for a single conservation law. To appear. · Zbl 0295.35051
[5] Guckenheimer, J., Solving a single conservation law. To appear. · Zbl 0306.35020
[6] Lax, P.D., Nonlinear hyperbolic equations. Comm. Pure Appl. Math. 6, 231–258 (1953). · Zbl 0050.31705
[7] Lax, P.D., Hyperbolic systems of conservation laws II. Comm. Pure Appl. Math. 10, 537–566 (1957). · Zbl 0081.08803
[8] Lax, P.D., Development of singularities of solutions of nonlinear hyperbolic partial differential equations. J. Math. Phys. 5, 611–613 (1964). · Zbl 0135.15101
[9] Lax, P.D., Shock Waves and Entropy, ”Contributions to Nonlinear Functional Analysis”, ed. E.A. Zarantonello, pp. 603–634. New York: Academic Press 1971.
[10] Schaeffer, D.G., A regularity theorem for conservation laws. Advances in Math. 11, 368–386 (1973) · Zbl 0267.35009
[11] Smoller, J.A., On the solution of the Riemann problem with general step data for an extended class of hyperbolic systems. Michigan Math. J. 16, 201–210 (1969). · Zbl 0185.34501
[12] Volpert, A.I., The spaces BV and quasilinear equations. Math. USSR Sb. 2, 257–267 (1967).
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.