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Transactions of the American Mathematical Society

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Questions of existence and uniqueness for hyperbolic equations with discontinuous coefficients


Authors: A. E. Hurd and D. H. Sattinger
Journal: Trans. Amer. Math. Soc. 132 (1968), 159-174
MSC: Primary 35.38
DOI: https://doi.org/10.1090/S0002-9947-1968-0222457-8
MathSciNet review: 0222457
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  • [1] Edward D. Conway, Generalized solutions of linear differential equations with discontinuous coefficients and the uniqueness question for multidimensional quasilinear conservation laws, J. Math. Anal. Appl. 18 (1967), 238–251. MR 0206474, https://doi.org/10.1016/0022-247X(67)90054-6
  • [2] R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
  • [3] I. M. Gelfand, Some questions of analysis and differential equations, Uspehi Mat. Nauk 14 (1959), no. 3 (87), 3-19; Amer. Math. Soc. Transl. (2) 26 (1963), 201-219.
  • [4] N. N. Kuznecov, On hyperbolic systems of linear equations with discontinuous coefficients, Ž. Vyčisl. Mat. i Mat. Fiz. 3 (1963), 299–313 (Russian). MR 0160039
  • [5] O. A. Oleĭnik, Discontinuous solutions of nonlinear differential equations, Uspehi Mat. Nauk 12 (1957), no. 3 (75), 3-73; Amer. Math. Soc. Transl. (2) 26 (1963), 95-172.

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DOI: https://doi.org/10.1090/S0002-9947-1968-0222457-8
Article copyright: © Copyright 1968 American Mathematical Society