The Cauchy problem for some class of hyperbolic differential operators with variable multiple characteristics

Kazuhiro YAMAMOTO

doi:10.2969/jmsj/03130481

Kazuhiro YAMAMOTO

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ジャーナルフリー

1979 年 31 巻 3 号 p. 481-502

DOI https://doi.org/10.2969/jmsj/03130481

詳細

Published: 1979 Received: 1977/10/22 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) J. Chazarain, Opérateurs hyperboliques à charactéristiques de multiplicité constante, Ann. Inst. Fourier (Grenoble), 24 (1974), 173-202.
2) H. Flaschka and G. Strang, The correctness of the Cauchy problem, Advances in Math., 6 (1971), 347-379.
3) L. Hörmander, Linear partial differential operators, Springer Verlag, Berlin, 1963.
4) L. Hörmander, The Cauchy problem for differential equations with double characteristics, J. D'analyse Math., 32 (1977), 118-196.
5) V. Ia. Ivrii, Sufficient conditions for regular and completely regular hyperbolicity, Trudy Moskov Math. Obšc., 33 (1975), 1-65.
6) V. Ia. Ivrii and V. M. Petkov, Necessary conditions for the correctness of the Cauchy problem for non-strictly hyperbolic equations, Uspehi Mat. Nauk, 29 (1974), 3-70.
7) K. Kitagawa and T. Sadamatsu, Une condition suffisante pour que le problème de Cauchy faiblement hyperbolique soit bien posé, to appear in J. Math. Kyoto Univ.
8) A. Lax, On Cauchy's problem for partial differential equations with multiple characteristics, Comm. Pure Appl. Math., 9 (1956), 135-169.
9) E.E. Levi, Caratteristiche multiple e problema di Cauchy, Ann. di Math., 16 (1909), 161-201.
10) A. Menikoff, The Cauchy problem for weakly hyperbolic equations, Amer. J. Math., 97 (1975), 548-558.
11) S. Mizohata and Y. Ohya, Sur la condition de E. E. Levi concernant des équations hyperbolique, Publ. Res. Inst. Math. Sci., Ser. A. 4 (1968), 511-526.
12) Y. Ohya, Le probleme de Cauchy à charactéristique multiples, to appear in Ann. Scuola Norm. Sup. Pisa.
13) O. A. Oleinik, On the Cauchy problem for weakly hyperbolic equations, Comm. Pure Appl. Math., 23 (1970), 569-586.
14) G. Paser, Hyperbolic equations with multiple characteristics and time dependent coefficients, SIAM J. Math. Anal., 2 (1971), 402-412.
15) V. M. Petkov, The Cauchy problem for a class of non-strictly hyperbolic equations with double characteristics, Serdica Bulg. Math. Publ., 1 (1975), 372-380.
16) M. Yamaguti, Le problème de Cauchy et les opérateurs d'intégrale singulière, Mem. Coll. Sci. Univ. Kyoto Ser. A Math., 32 (1959), 121-151.
17) K. Yamamoto, Cauchy problem for hyperbolic operators with variable multiple characteristics, Proc. Amer. Math. Soc., 72 (1978), 109-116.
18) M. Zeman, The well-posedness of the Cauchy problem for partial differential equations with multiple characteristics, Comm. in Partial Diff. Equations, 2 (1977), 223-249.

Right : [1] J. Chazarain, Opérateurs hyperboliques à charactéristiques de multiplicité constante, Ann. Inst. Fourier (Grenoble), 24 (1974), 173-202.
[2] H. Flaschka and G. Strang, The correctness of the Cauchy problem, Advances in Math., 6 (1971), 347-379.
[3] L. Hörmander, Linear partial differential operators, Springer Verlag, Berlin, 1963.
[4] L. Hörmander, The Cauchy problem for differential equations with double characteristics, J. D'analyse Math., 32 (1977), 118-196.
[5] V. Ia. Ivrii, Sufficient conditions for regular and completely regular hyperbolicity, Trudy Moskov Math. Obšc., 33 (1975), 1-65.
[6] V. Ia. Ivrii and V. M. Petkov, Necessary conditions for the correctness of the Cauchy problem for non-strictly hyperbolic equations, Uspehi Mat. Nauk, 29 (1974), 3-70.
[7] K. Kitagawa and T. Sadamatsu, Une condition suffisante pour que le problème de Cauchy faiblement hyperbolique soit bien posé, to appear in J. Math. Kyoto Univ.
[8] A. Lax, On Cauchy's problem for partial differential equations with multiple characteristics, Comm. Pure Appl. Math., 9 (1956), 135-169.
[9] E. E. Levi, Caratteristiche multiple e problema di Cauchy, Ann. di Math., 16 (1909), 161-201.
[10] A. Menikoff, The Cauchy problem for weakly hyperbolic equations, Amer. J. Math., 97 (1975), 548-558.
[11] S. Mizohata and Y. Ohya, Sur la condition de E. E. Levi concernant des équations hyperbolique, Publ. Res. Inst. Math. Sci., Ser. A. 4 (1968), 511-526.
[12] Y. Ohya, Le probleme de Cauchy à charactéristique multiples, to appear in Ann. Scuola Norm. Sup. Pisa.
[13] O. A. Oleinik, On the Cauchy problem for weakly hyperbolic equations, Comm. Pure Appl. Math., 23 (1970), 569-586.
[14] G. Paser, Hyperbolic equations with multiple characteristics and time dependent coefficients, SIAM J. Math. Anal., 2 (1971), 402-412.
[15] V. M. Petkov, The Cauchy problem for a class of non-strictly hyperbolic equations with double characteristics, Serdica Bulg. Math. Publ., 1 (1975), 372-380.
[16] M. Yamaguti, Le problème de Cauchy et les opérateurs d'intégrale singulière, Mem. Coll. Sci. Univ. Kyoto Ser. A Math., 32 (1959), 121-151.
[17] K. Yamamoto, Cauchy problem for hyperbolic operators with variable multiple characteristics, Proc. Amer. Math. Soc., 72 (1978), 109-116.
[18] M. Zeman, The well-posedness of the Cauchy problem for partial differential equations with multiple characteristics, Comm. in Partial Diff. Equations, 2 (1977), 223-249.

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

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