Singular hyperbolic systems, VI Asymptotic analysis for Fuchsian hyperbolic equations in Gevrey classes

Hidetoshi TAHARA

doi:10.2969/jmsj/03940551

Singular hyperbolic systems, VI

Asymptotic analysis for Fuchsian hyperbolic equations in Gevrey classes

Hidetoshi TAHARA

著者情報

ジャーナルフリー

1987 年 39 巻 4 号 p. 551-580

DOI https://doi.org/10.2969/jmsj/03940551

詳細

Published: 1987 Received: 1986/03/22 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) M. S. Baouendi and C. Goulaouic, Cauchy problems with characteristic initial hypersurface, Comm. Pure Appl. Math., 26 (1973), 455-475.
2) A. Bove, J. E. Lewis and C. Parenti, Structure properties of solutions of some Fuchsian hyperbolic equations, Math. Ann., 273 (1986), 553-571.
3) K. Igari, An admissible data class of the Cauchy problem for non-strictly hyperbolic operators, J. Math. Kyoto Univ., 21 (1981), 351-373.
4) V. Ja. Ivrii, Cauchy problem conditions for hyperbolic operators with characteristics of variable multiplicity for Gevrey classes, Sibirsk. Mat. Zh., 17 (1976), 1256-1270.
5) H. Komatsu, Ultradistributions, I. Structure theorems and a characterization, J. Fac. Sci Univ. Tokyo Sect. IA Math., 20 (1973), 25-105.
6) J. Leray and Y. Ohya, Systèmes linéaires, hyperboliques non stricts, Colloque CBRM, 1964, 105-144.
7) T. Mandai, Necessary conditions for well-posedness of the flat Cauchy problem and the regularity loss of solutions, Publ. RIMS, Kyoto Univ., 19 (1983), 145-168.
8) T. Mandai, Generalized Levi conditions for weakly hyperbolic equations -an attempt to treat the degeneracy with respect to the space variables-, Publ. RIMS, Kyoto Univ., 22 (1986), 1-23.
9) S. Mizohata, The theory of partial differential equations, Cambridge Univ. Press, 1973.
10) H. Tahara, Fuchsian type equations and Fuchsian hyperbolic equations, Japan. J. Math. New Ser., 5 (1979), 245-347.
11) H. Tahara, Singular hyperbolic systems, III. On the Cauchy problem for Fuchsian hyperbolic partial differential equations, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 27 (1980), 465-507.
12) H. Tahara, Singular hyperbolic systems, V. Asymptotic expansions for Fuchsian hyperbolic partial differential equations, J. Math. Soc. Japan, 36 (1984), 449-473.
13) H. Tahara, On Fuchsian hyperbolic partial differential equations, Lecture Notes in Math., Springer, No. 1223 (1986), 243-253, Proceedings of the Conference on “Differential Equations in Banach Spaces” held on July 2-5, 1985, at the University of Bologna (Italia).
14) H. Tahara, Cauchy problems for Fuchsian hyperbolic equations in spaces of functions of Gevrey classes, Proc. Japan Acad., 61A (1985), 63-65.
15) H. Tahara, Asymptotic expansions of solutions of Fuchsian hyperbolic equations in spaces of functions of Gevrey classes, Proc. Japan Acad., 61A (1985), 255-258.
16) H. Uryu, Conditions for well-posedness in Gevrey classes of the Cauchy problems for Fuchsian hyperbolic operators, Publ. RIMS, Kyoto Univ., 21 (1985), 355-383.
17) W. Wasow, Asymptotic expansions for ordinary differential equations, Interscience, 1965.

Right : [1] M. S. Baouendi and C. Goulaouic, Cauchy problems with characteristic initial hypersurface, Comm. Pure Appl. Math., 26 (1973), 455-475.
[2] A. Bove, J. E. Lewis and C. Parenti, Structure properties of solutions of some Fuchsian hyperbolic equations, Math. Ann., 273 (1986), 553-571.
[3] K. Igari, An admissible data class of the Cauchy problem for non-strictly hyperbolic operators, J. Math. Kyoto Univ., 21 (1981), 351-373.
[4] V. Ja. Ivrii, Cauchy problem conditions for hyperbolic operators with characteristics of variable multiplicity for Gevrey classes, Sibirsk. Mat. Zh., 17 (1976), 1256-1270.
[5] H. Komatsu, Ultradistributions, I. Structure theorems and a characterization, J. Fac. Sci Univ. Tokyo Sect. IA Math., 20 (1973), 25-105.
[6] J. Leray and Y. Ohya, Systèmes linéaires, hyperboliques non stricts, Colloque CBRM, 1964, 105-144.
[7] T. Mandai, Necessary conditions for well-posedness of the flat Cauchy problem and the regularity loss of solutions, Publ. RIMS, Kyoto Univ., 19 (1983), 145-168.
[8] T. Mandai, Generalized Levi conditions for weakly hyperbolic equations -an attempt to treat the degeneracy with respect to the space variables-, Publ. RIMS, Kyoto Univ., 22 (1986), 1-23.
[9] S. Mizohata, The theory of partial differential equations, Cambridge Univ. Press, 1973.
[10] H. Tahara, Fuchsian type equations and Fuchsian hyperbolic equations, Japan. J. Math. New Ser., 5 (1979), 245-347.
[11] H. Tahara, Singular hyperbolic systems, III. On the Cauchy problem for Fuchsian hyperbolic partial differential equations, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 27 (1980), 465-507.
[12] H. Tahara, Singular hyperbolic systems, V. Asymptotic expansions for Fuchsian hyperbolic partial differential equations, J. Math. Soc. Japan, 36 (1984), 449-473.
[13] H. Tahara, On Fuchsian hyperbolic partial differential equations, Lecture Notes in Math., Springer, No. 1223 (1986), 243-253, Proceedings of the Conference on “Differential Equations in Banach Spaces” held on July 2-5, 1985, at the University of Bologna (Italia).
[14] H. Tahara, Cauchy problems for Fuchsian hyperbolic equations in spaces of functions of Gevrey classes, Proc. Japan Acad., 61A (1985), 63-65.
[15] H. Tahara, Asymptotic expansions of solutions of Fuchsian hyperbolic equations in spaces of functions of Gevrey classes, Proc. Japan Acad., 61A (1985), 255-258.
[16] H. Uryu, Conditions for well-posedness in Gevrey classes of the Cauchy problems for Fuchsian hyperbolic operators, Publ. RIMS, Kyoto Univ., 21 (1985), 355-383.
[17] W. Wasow, Asymptotic expansions for ordinary differential equations, Interscience, 1965.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

責任著者(Corresponding author)

訂正情報

J-STAGEへの登録はこちら（無料）