no. 2
Well-posedness in the Gevrey classes of the Cauchy problem for a non-strictly hyperbolic equation with coefficients depending on time
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 10 (1983) no. 2, pp. 291-312. 
@article{ASNSP_1983_4_10_2_291_0,
     author = {Colombini, F. and Jannelli, E. and Spagnolo, S.},
     title = {Well-posedness in the {Gevrey} classes of the {Cauchy} problem for a non-strictly hyperbolic equation with coefficients depending on time},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {291--312},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 10},
     number = {2},
     year = {1983},
     mrnumber = {728438},
     zbl = {0543.35056},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1983_4_10_2_291_0/}
}
TY  - JOUR
AU  - Colombini, F.
AU  - Jannelli, E.
AU  - Spagnolo, S.
TI  - Well-posedness in the Gevrey classes of the Cauchy problem for a non-strictly hyperbolic equation with coefficients depending on time
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1983
SP  - 291
EP  - 312
VL  - 10
IS  - 2
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_1983_4_10_2_291_0/
LA  - en
ID  - ASNSP_1983_4_10_2_291_0
ER  - 
%0 Journal Article
%A Colombini, F.
%A Jannelli, E.
%A Spagnolo, S.
%T Well-posedness in the Gevrey classes of the Cauchy problem for a non-strictly hyperbolic equation with coefficients depending on time
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1983
%P 291-312
%V 10
%N 2
%I Scuola normale superiore
%U http://www.numdam.org/item/ASNSP_1983_4_10_2_291_0/
%G en
%F ASNSP_1983_4_10_2_291_0
Colombini, F.; Jannelli, E.; Spagnolo, S. Well-posedness in the Gevrey classes of the Cauchy problem for a non-strictly hyperbolic equation with coefficients depending on time. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 10 (1983) no. 2, pp. 291-312. http://www.numdam.org/item/ASNSP_1983_4_10_2_291_0/

[1] F. Colombini - E. De Giorgi - S. Spagnolo, Sur les équations hyperboliques avec des coefficients qui ne dépendent que du temps, Ann. Scuola Norm. Sup. Pisa, 6 (1979), pp. 511-559. | Numdam | MR | Zbl

[2] F. Colombini - S. Spagnolo, An example of weakly hyperbolic Cauchy problem not well posed in C∞, Acta Math., 148 (1982), pp. 243-253. | Zbl

[3] J. Dieudonné, Sur un théorème de Glaeser, J. Analyse Math., 23 (1970), pp. 85-88. | MR | Zbl

[4] G. Glaeser, Racine carrée d'une function differentiable, Ann. Inst. Fourier, 13 (1963), pp. 203-210. | Numdam | MR | Zbl

[5] V. Ya. IVRII - V.M. Petkov, Necessary conditions for the Cauchy problem for non-strictly hyperbolic equations to be well-posed, Uspehi Mat. Nauk, 29 (1974), pp. 3-70, English Transl. in Russian Math. Surveys. | MR | Zbl

[6] E. Jannelli, Weakly hyperbolic equations of second order with coefficients real analytic in space variables, Comm. in Partial Diff. Equations, 7 (1982), pp. 537-558. | MR | Zbl

[7] T. Nishitani, The Cauchy problem for weakly hyperbolic equations of second order, Comm. in Partial Diff. Equations, 5 (1980), pp. 1273-1296. | MR | Zbl

[8] O.A. Oleinik, On the Cauchy problem for weakly hyperbolic equations, Comm. Pure Appl. Math., 23 (1970), pp. 569-586. | MR