References
Federer, H., Geometric Measure Theory. New York: Springer 1969.
Glimm, J., Solutions in the large for nonlinear hyperbolic systems of conservation laws. Comm. Pure Appl. Math. 18, 697–715 (1965).
Glimm, J., & P.D. Lax, Decay of solutions of nonlinear hyperbolic conservation laws. Mem. Amer. Math. Soc. 101 (1970).
Golubitsky, M, & D.G. Schaeffer, Stability of shock waves for a single conservation law. To appear.
Guckenheimer, J., Solving a single conservation law. To appear.
Lax, P.D., Nonlinear hyperbolic equations. Comm. Pure Appl. Math. 6, 231–258 (1953).
Lax, P.D., Hyperbolic systems of conservation laws II. Comm. Pure Appl. Math. 10, 537–566 (1957).
Lax, P.D., Development of singularities of solutions of nonlinear hyperbolic partial differential equations. J. Math. Phys. 5, 611–613 (1964).
Lax, P.D., Shock Waves and Entropy, “Contributions to Nonlinear Functional Analysis”, ed. E.A. Zarantonello, pp. 603–634. New York: Academic Press 1971.
Schaeffer, D.G., A regularity theorem for conservation laws. Advances in Math. 11, 368–386 (1973)
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).
Volpert, A.I., The spaces BV and quasilinear equations. Math. USSR Sb. 2, 257–267 (1967).
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Communicated by C. Dafermos
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Diperna, R.J. Singularities of solutions of nonlinear hyperbolic systems of conservation laws. Arch. Rational Mech. Anal. 60, 75–100 (1975). https://doi.org/10.1007/BF00281470
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DOI: https://doi.org/10.1007/BF00281470