Characteristic Cauchy problems for some non-Fuchsian partial differential operators

Takeshi MANDAI

doi:10.2969/jmsj/04530511

Takeshi MANDAI

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JOURNAL FREE ACCESS

1993 Volume 45 Issue 3 Pages 511-545

DOI https://doi.org/10.2969/jmsj/04530511

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Published: 1993 Received: December 02, 1991 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: 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) M. S. Baouendi and C. Goulaouic, Cauchy problems with multiple characteristics in spaces of regular distributions, Russian Math. Surveys, 29 (1974), 72-78.
3) J. Elschner, Singular Ordinary Differential Operators and Pseudodifferential Equations, Lecture Notes in Math., 1128, Springer-Verlag, 1985.
4) Y. Hasegawa, On the initial value problems with data on a double characteristic, J. Math. Kyoto Univ., 11 (1971), 357-372.
5) A. N. Kuznetsov, Differentiable solutions to degenerate systems of ordinary equations, Funct. Anal. Appl., 6 (1972), 119-127.
6) Y. Laurent, Calcul d'indices et irrégularité pour les systèmes holonomes, Astérisque, 130, Soc. Math. France, 1985, pp. 352-364.
7) B. Malgrange, Sur la réduction formelle des équations différentielles à singularités irrégulières, Notas multigraphiées, Grenoble, 1979.
8) T. Mandai, Existence and non-existence of null-solutions for some non-Fuchsian partial differential operators with t-dependent coefficients, Nagoya Math. J., 122 (1991), 115-137.
9) T. Mandai, Existence of C^∞ null-solutions and behavior of bicharacteristic curves for differential operators with C^∞ coefficients, Japan. J. Math., 15 (1989), 53-63.
10) T. Mandai, A necessary and sufficient condition for the well-posedness of some weakly hyperbolic Cauchy problems, Comm. Partial Differential Equations, 8 (1983), 735-771.
11) M. Miyake, Newton polygons and formal Gevrey indices in the Cauchy-Goursat- Fuchs type equations, J. Math. Soc. Japan, 43 (1991), 305-330.
12) S. Ouchi, Existence of singular solutions and null solutions for linear partial differential operators, J. Fac. Sri. Univ. Tokyo Sect. IA Math., 32 (1985), 457-498.
13) A. Yonemura, Newton polygons and formal Gevrey classes, Publ. Res. Inst. Math. Sci., Kyoto Univ., 26 (1990), 197-204.

Right : [1] M. S. Baouendi and C. Goulaouic, Cauchy problems with characteristic initial hypersurface, Comm. Pure Appl. Math., 26 (1973), 455-475.
[2] M. S. Baouendi and C. Goulaouic, Cauchy problems with multiple characteristics in spaces of regular distributions, Russian Math. Surveys, 29 (1974), 72-78.
[3] J. Elschner, Singular Ordinary Differential Operators and Pseudodifferential Equations, Lecture Notes in Math., 1128, Springer-Verlag, 1985.
[4] Y. Hasegawa, On the initial value problems with data on a double characteristic, J. Math. Kyoto Univ., 11 (1971), 357-372.
[5] A. N. Kuznetsov, Differentiable solutions to degenerate systems of ordinary equations, Funct. Anal. Appl., 6 (1972), 119-127.
[6] Y. Laurent, Calcul d'indices et irrégularité pour les systèmes holonomes, Astérisque, 130, Soc. Math. France, 1985, pp. 352-364.
[7] B. Malgrange, Sur la réduction formelle des équations différentielles à singularités irrégulières, Notas multigraphiées, Grenoble, 1979.
[8] T. Mandai, Existence and non-existence of null-solutions for some non-Fuchsian partial differential operators with t-dependent coefficients, Nagoya Math. J., 122 (1991), 115-137.
[9] T. Mandai, Existence of C^∞ null-solutions and behavior of bicharacteristic curves for differential operators with C^∞ coefficients, Japan. J. Math., 15 (1989), 53-63.
[10] T. Mandai, A necessary and sufficient condition for the well-posedness of some weakly hyperbolic Cauchy problems, Comm. Partial Differential Equations, 8 (1983), 735-771.
[11] M. Miyake, Newton polygons and formal Gevrey indices in the Cauchy-Goursat-Fuchs type equations, J. Math. Soc. Japan, 43 (1991), 305-330.
[12] S. Ouchi, Existence of singular solutions and null solutions for linear partial differential operators, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 32 (1985), 457-498.
[13] A. Yonemura, Newton polygons and formal Gevrey classes, Publ. Res. Inst. Math. Sci., Kyoto Univ., 26 (1990), 197-204.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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