On global real analytic solutions of the degenerate Kirchhoff equation

Kunihiko Kajitani; Kaoru Yamaguti

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1994)

  • Volume: 21, Issue: 2, page 279-297
  • ISSN: 0391-173X

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Kajitani, Kunihiko, and Yamaguti, Kaoru. "On global real analytic solutions of the degenerate Kirchhoff equation." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 21.2 (1994): 279-297. <http://eudml.org/doc/84178>.

@article{Kajitani1994,
author = {Kajitani, Kunihiko, Yamaguti, Kaoru},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Kirchhoff model for the vibrating string; global well-posedness in the class of real analytic functions},
language = {eng},
number = {2},
pages = {279-297},
publisher = {Scuola normale superiore},
title = {On global real analytic solutions of the degenerate Kirchhoff equation},
url = {http://eudml.org/doc/84178},
volume = {21},
year = {1994},
}

TY - JOUR
AU - Kajitani, Kunihiko
AU - Yamaguti, Kaoru
TI - On global real analytic solutions of the degenerate Kirchhoff equation
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1994
PB - Scuola normale superiore
VL - 21
IS - 2
SP - 279
EP - 297
LA - eng
KW - Kirchhoff model for the vibrating string; global well-posedness in the class of real analytic functions
UR - http://eudml.org/doc/84178
ER -

References

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  1. [1] L. Arosio - S. Spagnolo, Global solution of the Cauchy problem for a nonlinear hyperbolic equation, Pitman Reseach Notes in Math. 109 (1984), 1-26. Zbl0598.35062MR772234
  2. [2] S. Bernstein, Sur une classe d'équations fonctionnelles aux dérivées partielles. Izv. Akad. Nauk SSSR, Ser. Mat.4 (1940), 17-26. Zbl0026.01901MR2699JFM66.0471.01
  3. [3] P. D'Ancona - S. Spagnolo, Global solvability for the degenerate Kirchhoff equation with real analytic data. Invent. Math.108 (1992), 247-246. Zbl0785.35067MR1161092
  4. [4] C. Fefferman - D.H. Phong, On positivity of pseudo-differential operators. Proc. Nat. Acad. Sci. USA75 (1978), 4677-4674. Zbl0391.35062MR507931
  5. [5] K. Kajitani, Global real analytic solution of the Cauchy problem for linear differential equations. Comm. P.D.E.11 (1984), 1489-1513. Zbl0628.35015MR862697
  6. [6] H. Kumano-Go, Pseudo-differential operators. MIT Press, Boston, 1981. Zbl0489.35003
  7. [7] S. Mizohata, Le problème de Cauchy pour les systèmes hyperboliques et paraboliqes. Memoirs of College of Sciences University of Kyoto32 (1959), 181-212. Zbl0095.29801MR123089
  8. [8] T. Nishida, Non linear vibration of an elastic string II. Preprint (1971). 
  9. [9] K. Nishihara, On a global solution of some quasilinear hyperbolic equations. Tokyo J. Math.7 (1984), 437-459. Zbl0586.35059MR776949
  10. [10] S.I. Pohozaev, On a class of quasilinear hyperbolic equations. Math. USSR-Sb.96 (1975), 152-166. Zbl0328.35060MR369938

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