Proceedings of the Japan Academy, Series A, Mathematical Sciences

Branching of singularities for degenerate hyperbolic operators and Stokes phenomena, II

Kazuo Amano and Gen Nakamura

Full-text: Open access

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 57, Number 3 (1981), 164-167.

Dates
First available in Project Euclid: 19 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1195516491

Digital Object Identifier
doi:10.3792/pjaa.57.164

Mathematical Reviews number (MathSciNet)
MR618083

Zentralblatt MATH identifier
0495.35052

Subjects
Primary: 35L80: Degenerate hyperbolic equations
Secondary: 35L67: Shocks and singularities [See also 58Kxx, 76L05]

Citation

Amano, Kazuo; Nakamura, Gen. Branching of singularities for degenerate hyperbolic operators and Stokes phenomena, II. Proc. Japan Acad. Ser. A Math. Sci. 57 (1981), no. 3, 164--167. doi:10.3792/pjaa.57.164. https://projecteuclid.org/euclid.pja/1195516491


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References

  • [1] S. Alinhac: Branching of singularities for a class of hyperbolic operators. Indiana Univ. Math. J., 27, 1027-1037 (1978).
  • [2] K. Amano: Branching of singularities for degenerate hyperbolic operators and Stokes phenomena. Proc. Japan Acad., 56A, 206-209 (1980).
  • [3] H. Kumano-go: Fourier integral operators and fundamental solutions of hyperbolic equations. Lecture Note Math., Tokyo Metropolitan University (1980) (in Japanese).
  • [4] G. Nakamura and H. Uryu: Parametrix of certain weakly hyperbolic operators. Comm. Partial Differential Equations, 5, 837-896 (1980).
  • [5] S. Nakane: Propagation of singularities and uniqueness in the Cauchy problem at a class of doubly characteristic points (to appear).
  • [6] K. Shinkai: On the fundamental solution for a degenerate hyperbolic system (to appear in Osaka J. Math.).
  • [7] K. Taniguchi and Y. Tozaki: A hyperbolic equation with double characteristics which has a solution with branching singularities. Math. Japon., 25, 279-300 (1980).
  • [8] H. Uryu: The Cauchy problem for weakly hyperbolic equations. Comm. Partial Differential Equations, 5, 23-40 (1980).
  • [9] A. Yoshikawa: Construction of a parametrix for the Cauchy problem of some weakly hyperbolic equation I. Hokkaido Math. J., 6, 313-344 (1977); ditto. II, ibid., 7, 1-26 (1978); ditto. Ill, ibid., 7, 127-141 (1978).

See also

  • Part I: Kazuo Amano. Branching of singularities for degenerate hyperbolic operators and Stokes phenomena. Proc. Japan Acad. Ser. A Math. Sci., Volume 56, Number 5 (1980), 206--209.
  • Part III: Kazuo Amano, Gen Nakamura. Branching of singularities for degenerate hyperbolic operator and Stokes phenomena, III. Proc. Japan Acad. Ser. A Math. Sci., Volume 58, Number 10 (1982), 432--435.
  • Part IV: Kazuo Amano, Gen Nakamura. Branching of singularities for degenerate hyperbolic operator and Stokes phenomena, IV. Proc. Japan Acad. Ser. A Math. Sci., Volume 59, Number 2 (1983), 47--50.