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Transactions of the American Mathematical Society

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On the regularity of the Riemann function for hyperbolic equations


Author: William L. Goodhue
Journal: Trans. Amer. Math. Soc. 175 (1973), 483-490
MSC: Primary 35L55
DOI: https://doi.org/10.1090/S0002-9947-1973-0318685-5
MathSciNet review: 0318685
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Abstract: In an earlier paper, A. Friedman demonstrated that the Riemann function for a strictly hyperbolic system with Gevrey coefficients was locally Gevrey of some higher order except along the bicharacteristics. By representing the Riemann function in terms of a progressing wave expansion, this result is extended beyond caustics.


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  • [1] R. Courant and P. D. Lax, The propagation of discontinuities in wave motion, Proc. Nat. Acad. Sci. U. S. A. 42 (1956), 872-876. MR 18, 399. MR 0081420 (18:399e)
  • [2] A. Friedman, Regularity of fundamental solutions of hyperbolic equations, Arch. Rational Mech. Anal. 11 (1962), 62-96. MR 26 #1624. MR 0144076 (26:1624)
  • [3] P. D. Lax, (a) Asymptotic solutions of oscillatory initial value problems, Duke Math. J. 24 (1957), 627-646. MR 20 #4096. (b) Lectures on hyperbolic differential equations, Stanford University, Stanford, Calif., 1963. MR 0097628 (20:4096)
  • [4] J. L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Vol. 3, Dunod, Paris, 1970. MR 0291887 (45:975)
  • [5] D. Ludwig, Exact and asymptotic solutions of the Cauchy problem, Atomic Energy Commission Research and Development Report NYO 2545.
  • [6] S. Mandelbrojt, Séries adhérentes régularisation des suites, applications, Gauthier-Villars, Paris, 1952. MR 14, 542. MR 0051893 (14:542f)
  • [7] C. Roumieu, Sur quelques extensions de la notion de distribution, Ann. Sci. École Norm. Sup. (3) 77 (1960), 41-121. MR 22 #12377. MR 0121643 (22:12377)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1973-0318685-5
Keywords: Riemann function, strictly hyperbolic systems, progressing wave expansion, Gevrey class
Article copyright: © Copyright 1973 American Mathematical Society

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