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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, (), Chap. V. 6
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