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Development of singularities in the nonlinear waves for quasi-linear hyperbolic partial differential equations. (English) Zbl 0379.35048


MSC:

35L60 First-order nonlinear hyperbolic equations
35B99 Qualitative properties of solutions to partial differential equations
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References:

[1] Glimm, J., Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math., 18, 697-715 (1965) · Zbl 0141.28902
[2] Glimm, J.; Lax, P. D., Decay of solutions of systems of nonlinear hyperbolic conservation laws, Mem. Amer. Math. Soc. No. 101 (1970) · Zbl 0204.11304
[3] John, F., Formation of singularities in one-dimensional nonlinear wave propagation, Comm. Pure Appl. Math., 27, 377-405 (1974) · Zbl 0302.35064
[4] Lax, P. D., Hyperbolic systems of conservation laws, II, Comm. Pure Appl. Math., 10, 537-556 (1957) · Zbl 0081.08803
[5] Lax, P. D., Development of singularities of solutions of nonlinear hyperbolic partial differential equations, J. Math. Phys., 5, 611-613 (1964) · Zbl 0135.15101
[6] Liu, T.-P, Linear and nonlinear large-time behavior of solutions of general systems of hyperbolic conservation laws, Comm. Pure Appl. Math., 30, 767-796 (1977) · Zbl 0358.35014
[7] Courant, R.; Hilbert, D., (Methods of Mathematical Physics, Vol. II (1962), Wiley: Wiley New York), Chap. V. 6 · Zbl 0729.00007
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