Global solvability for the degenerate Kirchhoff equation

Fumihiko Hirosawa

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1998)

  • Volume: 26, Issue: 1, page 75-95
  • ISSN: 0391-173X

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Hirosawa, Fumihiko. "Global solvability for the degenerate Kirchhoff equation." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 26.1 (1998): 75-95. <http://eudml.org/doc/84324>.

@article{Hirosawa1998,
author = {Hirosawa, Fumihiko},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {degenerate elliptic operator},
language = {eng},
number = {1},
pages = {75-95},
publisher = {Scuola normale superiore},
title = {Global solvability for the degenerate Kirchhoff equation},
url = {http://eudml.org/doc/84324},
volume = {26},
year = {1998},
}

TY - JOUR
AU - Hirosawa, Fumihiko
TI - Global solvability for the degenerate Kirchhoff equation
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1998
PB - Scuola normale superiore
VL - 26
IS - 1
SP - 75
EP - 95
LA - eng
KW - degenerate elliptic operator
UR - http://eudml.org/doc/84324
ER -

References

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  2. [2] A. Arosio - S. Spagnolo, Global solution to the Cauchy problem for a nonlinear equation, Pitman Res. Notes Math.109 (1984), 1-26. Zbl0598.35062MR772234
  3. [3] S. Bernstein, Sur une class d'équations fonctionnelles aux dérivées partielles, Izv. Akad. Nauk SSSR, Ser. Mat.4 (1940), 17-26. Zbl0026.01901MR2699JFM66.0471.01
  4. [4] P. D'Ancona, Gevrey well posedness of an abstract Cauchy problem of weakly hyperbolic type, Publ. Res. Inst. Math. Sci, Kyoto Univ.24 (1988), 433-449. Zbl0706.35077MR966182
  5. [5] P. D'Ancona - S. Spagnolo, Global solvability for the degenerate Kirchhoff equation with real analytic data, Invent. Math.108 (1992), 247-262. Zbl0785.35067MR1161092
  6. [6] G.H. Hardy - J.E. Littlewood - G. Polya, "Inequalities", Cambridge UP, Cambridge, 1952. Zbl0047.05302MR46395
  7. [7] F. Hirosawa, Global solvability for the generalized degenerate Kirchhoff equation with real-analytic data in Rn, Tsukuba J. Math.21 (1997), 483-503. Zbl0896.35073MR1473934
  8. [8] T. Kinoshita, On the wellposedness in the ultradifferentiable classes of the Cauchy ploblem for a weakly hyperbolic equation of second order, Tsukuba J. Math. (to appear). Zbl0942.35104MR1637629
  9. [9] K. Kajitani - K. Yamaguti, On global real analytic solutions of the degenerate Kirchhoff equation, Ann. Scuola Norm. Sup. Pisa. Cl. Sci. (4) 21 (1994), 279-297. Zbl0819.35099MR1288368
  10. [10] G. Krantz - H.R. Parks, "A Primer of Real Analytic Functions", Birkhäuser Verlag, Basel - Boston - Berlin, 1992. Zbl0767.26001MR1182792
  11. [11] W. Matsumoto, Theory of pseudo-differential operators of ultradifferentiable class, J. Math. Kyoto Univ.27 (1987), 453-500. Zbl0651.35088MR910230
  12. [12] T. Nishida, A note on the nonlinear vibrations of the elastic string, Mem. Fac. Engrg. Kyoto Univ.33 (1971), 329-341. MR279387
  13. [13] K. Nishihara, On a global solution of some quasilinear hyperbolic equation, Tokyo J. Math.7 (1984), 437-459. Zbl0586.35059MR776949
  14. [14] G. Perla, On classical solutions of a quasilinear hyperbolic equation, Nonlinear Anal.3 (1979), 613-627. Zbl0419.35062MR541872
  15. [15] O.A. Oleinik, On linear equations of second order with non-negative characteristic form, Mat. Sb. N.S.69 (1966),111-140 (English translation: Transl. Amer. Mat. Soc.65,167-199). MR193383
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  17. [17] K. Yamaguti, On global quasi-analytic solution of the degenerate Kirchhoff equation, Tsukuba J. Math. (to appear). Zbl1028.35090MR1603843

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