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Piecewise smooth solutions of a single conservation law exist. (English) Zbl 0418.35021

MSC:
35B65 Smoothness and regularity of solutions to PDEs
35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
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[1] Lax, P.D., Weak solutions of nonlinear hyperbolic equations and their numerical computations, Comm. pure appl. math., 7, 159-193, (1954) · Zbl 0055.19404
[2] Lax, P.D., Hyperbolic systems of conservation laws, II, Comm. pure appl. math., 10, 537-566, (1957) · Zbl 0081.08803
[3] Keyfitz, B., Time decreasing functionals of nonlinear conservation laws, Comm. pure appl. math., 24, 125-131, (1971)
[4] Oleinik, O.A., Uniqueness and stability of the generalized solution of the Cauchy problem for a quasi-linear equation, Uspehi mat. nauk., 86, No. 2, 165-170, (1959), English transl. in Amer. Math. Soc. Trans. Ser. 2, No. 33, 285-290.
[5] Schaeffer, D.G., A regularity theorem for conservation laws, Advances in math., 11, 368-386, (1973) · Zbl 0267.35009
[6] Golubitsky, M.; Schaeffer, D.G., Stability of shock waves for a single conservation law, Advances in math, 15, 65-71, (1975) · Zbl 0295.35051
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