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An asymptotic method for a singular hyperbolic equation. (English) Zbl 0221.35049


MSC:

35L60 First-order nonlinear hyperbolic equations
35C20 Asymptotic expansions of solutions to PDEs
35Q05 Euler-Poisson-Darboux equations
76N15 Gas dynamics (general theory)
86A05 Hydrology, hydrography, oceanography
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References:

[1] Ho, D. V., & R. E. Meyer, J. Fluid Mech. 14, 305 (1962). · Zbl 0116.43403 · doi:10.1017/S0022112062001251
[2] Whitham, G. B., J. Fluid Mech. 4, 337 (1958). · Zbl 0081.41501 · doi:10.1017/S0022112058000495
[3] Hayes, W. D., & R. F. Probstein, Hypersonic Flow Theory. New York: Academic Press 1959. · Zbl 0084.42202
[4] Sakurai, A., Commun. Pure Appl. Math. 13, 353 (1960). · Zbl 0099.41503 · doi:10.1002/cpa.3160130303
[5] Shen, M. C., & R. E. Meyer, J. Fluid Mech. 16, 108 (1963). · doi:10.1017/S0022112063000616
[6] Keller, H. B., D. A. Levine, & G. B. Whitham, J. Fluid Mech. 7, 302 (1960). · Zbl 0090.43302 · doi:10.1017/S002211206000150X
[7] Meyer, R. E., Uniformisation of a Quasi-linear Hyperbolic Equation, Part I. J. Math. Mech. (1966).
[8] Meyer, R. E., & A. D. Taylor, J. Geophys. Res. 68, 6443 (1963). · doi:10.1029/JZ068i024p06443
[9] Stoker, J. J., Water Waves. New York: Interscience Publ. 1957.
[10] Lax, P. D., Commun. Pure Appl. Math. 10, 537 (1957). · Zbl 0081.08803 · doi:10.1002/cpa.3160100406
[11] Courant, R., & D. Hilbert, Methods of Mathematical Physics, Vol. II. New York: Interscience Publ. 1962. · Zbl 0099.29504
[12] Chen, Y. W., Commun. Pure Appl. Math. 6, 179 (1953). · Zbl 0053.14604 · doi:10.1002/cpa.3160060203
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