The Cauchy problem for semilinear weakly hyperbolic equations in Hilbert spaces
D'Ancona, Piero
Annales de l'I.H.P. Analyse non linéaire, Tome 11 (1994), p. 343-358 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1994-01-01
@article{AIHPC_1994__11_4_343_0,
     author = {d'Ancona, Piero},
     title = {The Cauchy problem for semilinear weakly hyperbolic equations in Hilbert spaces},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {11},
     year = {1994},
     pages = {343-358},
     mrnumber = {1287237},
     zbl = {0836.34064},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1994__11_4_343_0}
}

D'Ancona, Piero. The Cauchy problem for semilinear weakly hyperbolic equations in Hilbert spaces. Annales de l'I.H.P. Analyse non linéaire, Tome 11 (1994) pp. 343-358. http://gdmltest.u-ga.fr/item/AIHPC_1994__11_4_343_0/

[A] T. Aubin, Nonlinear analysis on Manifolds. Monge-Ampère equations, Springer, Berlin, 1982. | MR 681859 | Zbl 0512.53044

[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. | MR 875159 | Zbl 0616.35049

[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. | MR 481322 | Zbl 0391.35006

[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. | MR 666112 | Zbl 0517.35053

[D] P. D'Ancona, On weakly hyperbolic equations in Hilbert spaces, to appear on Funkcialaj Ekvacioj1994. | Zbl 0829.34045

[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.

[K] T. Kato, Abstract differential equations and nonlinear mixedproblems, Lezioni Fermiane, Scuola Normale Superiore, Pisa, 1985. | Zbl 0648.35001

[L1] J.-L. Lions, Remarks on evolution inequalities, J. Math. Soc. Japan, 18, 1966, pp. 331-342. | MR 216345 | Zbl 0173.12901

[L2] J.-L. Lions, Equations différentielles opérationnelles et problèmes aux limites, Grundlehren der Mathematischen Wissenschaft, 111, Springer, Berlin, 1961. | MR 153974 | Zbl 0098.31101

[LM] J.-L. Lions, and E. Magenes, Non-homogeneous boundary value problems and applications, Springer, Berlin, 1973. | MR 350179 | Zbl 0251.35001

[Ni] L. Nirenberg, An abstract form of the Cauchy Kowalewski theorem, J. Diff. Geom., 6, 1972, pp. 561-576. | MR 322321 | Zbl 0257.35001

[O] O. Oleinik, On the Cauchy problem for weakly hyperbolic equations, Comm. Pure Appl. Math., 23, 1970, pp. 569-586. | MR 264227 | Zbl 0193.38602

[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]. | MR 285941 | Zbl 0234.35018

[Y] T. Yamanaka, Note on Kowalewskaja's system of partial differential equations, Comment. Math. Univ. St. Paul, 9, 1961, pp. 7-10. | MR 126044 | Zbl 0122.35302