Singular hyperbolic systems, V. Asymptotic expansions for Fuchsian hyperbolic partial differential equations

Hidetoshi TAHARA

doi:10.2969/jmsj/03630449

Hidetoshi TAHARA

著者情報

ジャーナルフリー

1984 年 36 巻 3 号 p. 449-473

DOI https://doi.org/10.2969/jmsj/03630449

詳細

Published: 1984 Received: 1983/07/28 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: 論文タイトル訂正内容: Wrong : Singular hyperbolic systems, V
Right : Singular hyperbolic systems, V. Asymptotic expansions for Fuchsian hyperbolic partial differential equations

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文サブタイトル訂正内容: Wrong : Asymptotic expansions for Fuchsian hyperbolic partial differential equations

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) Chi Min-You, On Fuchsian type partial differential equations, Sci. Rep. Wuhan Univ., 4 (1977), 1-6 (Chinese).
3) V. Kh. Froim, Linear scalar partial differential equations with regular singularities on a hypersurface, Differencial'nye Uravnenija, 9-3 (1973), 533-541 (Russian).
4) S. Mizohata, The theory of partial differential equations, Cambridge Univ. Press, 1973.
5) O. A. Repin, Determination of the general solution and solution of the Cauchy problem for an equation of hyperbolic type, Differencial'nye Uravnenija (Ryazan), 6 (1975), 155-161 (Russian).
6) R. Sakamoto, Cauchy problem for degenerate hyperbolic equations, Comm. Pure Appl. Math., 33 (1980), 785-816.
7) H. Tahara, Fuchsian type equations and Fuchsian hyperbolic equations, Japan. J. Math. New Ser., 5 (1979), 245-347.
8) H. Tahara, Fundamental systems of analytic solutions of Fuchsian type partial differential equations, Funkcialaj Ekvacioj, 24 (1981), 135-140.
9) H. Tahara, Singular hyperbolic systems. I. Existence, uniqueness and differentiability, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 26 (1979), 213-238. II. Pseudo-differential operators with a parameter and their applications to singular hyperbolic systems, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 26 (1979), 391-412. III. On the Cauchy problem for Fuchsian hyperbolic partial differential equations, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 27 (1980), 465-507. IV. Remarks on the Cauchy problem for singular hyperbolic partial differential equations, Japan. J. Math. New Ser., 8 (1982), 297-308.
10) H. Tahara, Asymptotic expansions of solutions of Fuchsian hyperbolic partial differential equations, Proc. Japan Acad., 59 (1983), 120-121.
11) S. A. Tersenov, On a singular Cauchy problem, Dokl. Akad. Nauk SSSR, 196 (1971), 1032-1035 (Russian).
12) W. Wasow, Asymptotic expansions for ordinary differential equations, Interscience, 1965.
13) A. Weinstein, The singular solutions and the Cauchy problem for generalized Tricomi equations, Comm. Pure Appl. Math., 7 (1954), 105-116.

Right : [1] M. S. Baouendi and C. Goulaouic, Cauchy problems with characteristic initial hypersurface, Comm. Pure Appl. Math., 26 (1973), 455-475.
[2] Chi Min-You, On Fuchsian type partial differential equations, Sci. Rep. Wuhan Univ., 4 (1977), 1-6 (Chinese).
[3] V. Kh. Froim, Linear scalar partial differential equations with regular singularities on a hypersurface, Differencial'nye Uravnenija, 9-3 (1973), 533-541 (Russian).
[4] S. Mizohata, The theory of partial differential equations, Cambridge Univ. Press, 1973.
[5] O. A. Repin, Determination of the general solution and solution of the Cauchy problem for an equation of hyperbolic type, Differencial'nye Uravnenija (Ryazan), 6 (1975), 155-161 (Russian).
[6] R. Sakamoto, Cauchy problem for degenerate hyperbolic equations, Comm. Pure Appl. Math., 33 (1980), 785-816.
[7] H. Tahara, Fuchsian type equations and Fuchsian hyperbolic equations, Japan. J. Math. New Ser., 5 (1979), 245-347.
[8] H. Tahara, Fundamental systems of analytic solutions of Fuchsian type partial differential equations, Funkcialaj Ekvacioj, 24 (1981), 135-140.
[9] H. Tahara, Singular hyperbolic systems. I. Existence, uniqueness and differentiability, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 26 (1979), 213-238. II. Pseudo-differential operators with a parameter and their applications to singular hyperbolic systems, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 26 (1979), 391-412. III. On the Cauchy problem for Fuchsian hyperbolic partial differential equations, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 27 (1980), 465-507. IV. Remarks on the Cauchy problem for singular hyperbolic partial differential equations, Japan. J. Math. New Ser., 8 (1982), 297-308.
[10] H. Tahara, Asymptotic expansions of solutions of Fuchsian hyperbolic partial differential equations, Proc. Japan Acad., 59 (1983), 120-121.
[11] S. A. Tersenov, On a singular Cauchy problem, Dokl. Akad. Nauk SSSR, 196 (1971), 1032-1035 (Russian).
[12] W. Wasow, Asymptotic expansions for ordinary differential equations, Interscience, 1965.
[13] A. Weinstein, The singular solutions and the Cauchy problem for generalized Tricomi equations, Comm. Pure Appl. Math., 7 (1954), 105-116.

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）