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The formation and decay of shocks for a conservation law in several dimensions. (English) Zbl 0352.35029

MSC:
35F20 Nonlinear first-order PDEs
35B99 Qualitative properties of solutions to partial differential equations
35B35 Stability in context of PDEs
76L05 Shock waves and blast waves in fluid mechanics
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[2] Conway, E. & J. Smoller, Global solutions of the Cauchy Problem for quasi-linear equations in several space variables, Comm. Pure Appl. Math., 19, 95-105 (1966). · Zbl 0138.34701 · doi:10.1002/cpa.3160190107
[3] Courant, R. & D. Hilbert, ?Methods of Mathematical Physics, Vol. II?, Interscience, New York, N.Y., 1962. · Zbl 0099.29504
[4] Gordon, W.B., On the diffeomorphisms of Euclidean Space, Amer. Math. Monthly, 79, 755-759 (1972). · Zbl 0263.57015 · doi:10.2307/2316266
[5] Kruzkov, S.N., First order equations in several space variables, Mat. Sbornik, 81 (123) (1970). English translation in Math. USSR-Sbornik, 10, 217-243 (1970).
[6] Lax, P.D., Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math., 10, 537-566 (1957) · Zbl 0081.08803 · doi:10.1002/cpa.3160100406
[7] Volpert, A.I., The spaces BV and quasilinear equations, Mat. Sbornik, 73 (115) (1967). English translation in Math. USSR-Sbornik, 2, 225-267 (1967).
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