Proceedings of the Japan Academy, Series A, Mathematical Sciences

The behaviour near the characteristic surface of singular solutions of linear partial differential equations in the complex domain

Sunao Ōuchi

Full-text: Open access

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 65, Number 4 (1989), 102-105.

Dates
First available in Project Euclid: 19 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1195512945

Digital Object Identifier
doi:10.3792/pjaa.65.102

Mathematical Reviews number (MathSciNet)
MR1011843

Zentralblatt MATH identifier
0706.35002

Subjects
Primary: 35G05: Linear higher-order equations
Secondary: 35A20: Analytic methods, singularities

Citation

Ōuchi, Sunao. The behaviour near the characteristic surface of singular solutions of linear partial differential equations in the complex domain. Proc. Japan Acad. Ser. A Math. Sci. 65 (1989), no. 4, 102--105. doi:10.3792/pjaa.65.102. https://projecteuclid.org/euclid.pja/1195512945


Export citation

References

  • [1] De Paris, J. C.: Probleme de Cauchy analytique a donnees singuleres pour un operateur differentiel bien decomposable. J. Math. Pures Appl., 51, 464-488 (1972).
  • [2] Hamada, Y.: The singularities of solutions of Cauchy problem. Publ. Res. Inst. Math. Sci. Kyoto Univ., 6, 21-40 (1969).
  • [3] Hamada, Y., Leray, J., et Wagshal, C.: Systemes d'equations aux derivees partielles a caracteristiques multiples; probleme de Cauchy ramifie; hyperbolicite partielle. J. Math. Pures Appl., 55, 297-352 (1976).
  • [4] Kashiwara, M. and Schapira, P.: Probleme de Cauchy pour les systemes microdifferentiels dans le domain complexe. Inv. Math., 46, 17-38 (1978).
  • [5] Ouchi, S.: Asymptotic behaviour of singular solutions of linear partial differential equations in the complex domain. J. Fac. Sci. Univ. Tokyo Sec. IA, Math., 27, 1-36 (1980).
  • [6] Ouchi, S.: An integral representation of singular solutions of linear partial differential equations in the complex domain, ibid., 27, 37-85 (1980).
  • [7] Ouchi, S.: Characteristic indices and subcharacteristic indices of surfaces for linear partial differential operators. Proc. Japan Acad., 57A, 481-484 (1981).
  • [8] Ouchi, S.: Index, localization and classification of characteristic surfaces for linear partial differential operators, ibid., 60A, 189-192 (1984).
  • [9] Ouchi, S.: Existence of singular solutions and null solutions for linear partial differential operators. J. Fac. Sci. Univ. Tokyo Sec. IA, Math., 32, 457-498 (1985).
  • [10] Ouchi, S.: Vanishing of singularities of solutions and an integral representation of singular solutions of linear partial differential equatons. Calcul d'operateurs et fronts d'ondes (ed. J. Vaillant). Hermann, Paris, pp. 168-177 (1988).
  • [11] Persson, J.: On the Cauchy problem in Cn wth singular data. Mathematiche, 30, 339-362 (1975).
  • [12] Wagschal, C.: Probleme de Cauchy analytique a donnees meromorphes. J. Math. Pures Appl., 51, 375-397 (1972).