The Cauchy problem for semilinear weakly hyperbolic equations in Hilbert spaces

Piero D'Ancona

Annales de l'I.H.P. Analyse non linéaire (1994)

  • Volume: 11, Issue: 4, page 343-358
  • ISSN: 0294-1449

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D'Ancona, Piero. "The Cauchy problem for semilinear weakly hyperbolic equations in Hilbert spaces." Annales de l'I.H.P. Analyse non linéaire 11.4 (1994): 343-358. <http://eudml.org/doc/78336>.

@article{DAncona1994,
author = {D'Ancona, Piero},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {abstract nonlinear second order equation; Olejnik's conditions; degenerate hyperbolic equations},
language = {eng},
number = {4},
pages = {343-358},
publisher = {Gauthier-Villars},
title = {The Cauchy problem for semilinear weakly hyperbolic equations in Hilbert spaces},
url = {http://eudml.org/doc/78336},
volume = {11},
year = {1994},
}

TY - JOUR
AU - D'Ancona, Piero
TI - The Cauchy problem for semilinear weakly hyperbolic equations in Hilbert spaces
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1994
PB - Gauthier-Villars
VL - 11
IS - 4
SP - 343
EP - 358
LA - eng
KW - abstract nonlinear second order equation; Olejnik's conditions; degenerate hyperbolic equations
UR - http://eudml.org/doc/78336
ER -

References

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  1. [A] T. Aubin, Nonlinear analysis on Manifolds. Monge-Ampère equations, Springer, Berlin, 1982. Zbl0512.53044MR681859
  2. [AS] A. Arosio and S. Spagnolo, Global existence for abstract evolution equations of weakly hyperbolic type, J. Math. pures et appl., 65, 1986, pp. 263-305. Zbl0616.35049MR875159
  3. [BG] M.S. Baouendi and C. Goulaouic, Remarks on the abstract form of nonlinear Cauchy-Kovalevsky theorems, Camm. Part. Diff. Equations, 2, 1977, pp. 1151-1162. Zbl0391.35006MR481322
  4. [CS] F. Colombini and S. Spagnolo, An example of a weakly hyperbolic Cauchy problem not well posed in C∞, Acta Math., 148, 1982, pp. 243- 253. Zbl0517.35053MR666112
  5. [D] P. D'Ancona, On weakly hyperbolic equations in Hilbert spaces, to appear on Funkcialaj Ekvacioj1994. Zbl0829.34045
  6. [DM] P.D.' Ancona and R. Manfrin, Local solvability for a class of weakly hyperbolic semilinear equations, to appear on Ann. Mat. pura e appl. 
  7. [K] T. Kato, Abstract differential equations and nonlinear mixedproblems, Lezioni Fermiane, Scuola Normale Superiore, Pisa, 1985. Zbl0648.35001
  8. [L1] J.-L. Lions, Remarks on evolution inequalities, J. Math. Soc. Japan, 18, 1966, pp. 331-342. Zbl0173.12901MR216345
  9. [L2] J.-L. Lions, Equations différentielles opérationnelles et problèmes aux limites, Grundlehren der Mathematischen Wissenschaft, 111, Springer, Berlin, 1961. Zbl0098.31101MR153974
  10. [LM] J.-L. Lions, and E. Magenes, Non-homogeneous boundary value problems and applications, Springer, Berlin, 1973. Zbl0251.35001MR350179
  11. [Ni] L. Nirenberg, An abstract form of the Cauchy Kowalewski theorem, J. Diff. Geom., 6, 1972, pp. 561-576. Zbl0257.35001MR322321
  12. [O] O. Oleinik, On the Cauchy problem for weakly hyperbolic equations, Comm. Pure Appl. Math., 23, 1970, pp. 569-586. MR264227
  13. [Ov] L.V. Ovčannikov, A nonlinear Cauchy problem in a scale of banach spaces, Doklad. Akad. Nauk SSSR, 200, 1971, pp.789-792 [transl.: Soviet. Math. Dokl., 12, 1971, pp. 1497-1502]. Zbl0234.35018MR285941
  14. [Y] T. Yamanaka, Note on Kowalewskaja's system of partial differential equations, Comment. Math. Univ. St. Paul, 9, 1961, pp. 7-10. Zbl0122.35302MR126044

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