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

Hidetoshi TAHARA

doi:10.2969/jmsj/03630449

Hidetoshi TAHARA

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1984 Volume 36 Issue 3 Pages 449-473

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

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Published: 1984 Received: July 28, 1983 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: TITLE Details: Wrong : Singular hyperbolic systems, V
Right : Singular hyperbolic systems, V. Asymptotic expansions for Fuchsian hyperbolic partial differential equations

Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Asymptotic expansions for Fuchsian hyperbolic partial differential equations

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: 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.

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