# Well-posedness in the Gevrey classes of the Cauchy problem for a non-strictly hyperbolic equation with coefficients depending on time

F. Colombini; E. Jannelli; S. Spagnolo

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1983)

- Volume: 10, Issue: 2, page 291-312
- ISSN: 0391-173X

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topColombini, F., Jannelli, E., and 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 10.2 (1983): 291-312. <http://eudml.org/doc/83908>.

@article{Colombini1983,

author = {Colombini, F., Jannelli, E., Spagnolo, S.},

journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},

keywords = {Cauchy problem; non-strict hyperbolicity; well posed; Gevrey class; Fourier-Laplace transform; approximate energy estimates},

language = {eng},

number = {2},

pages = {291-312},

publisher = {Scuola normale superiore},

title = {Well-posedness in the Gevrey classes of the Cauchy problem for a non-strictly hyperbolic equation with coefficients depending on time},

url = {http://eudml.org/doc/83908},

volume = {10},

year = {1983},

}

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

PB - Scuola normale superiore

VL - 10

IS - 2

SP - 291

EP - 312

LA - eng

KW - Cauchy problem; non-strict hyperbolicity; well posed; Gevrey class; Fourier-Laplace transform; approximate energy estimates

UR - http://eudml.org/doc/83908

ER -

## References

top- [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. Zbl0417.35049MR553796
- [2] F. Colombini - S. Spagnolo, An example of weakly hyperbolic Cauchy problem not well posed in C∞, Acta Math., 148 (1982), pp. 243-253. Zbl0517.35053
- [3] J. Dieudonné, Sur un théorème de Glaeser, J. Analyse Math., 23 (1970), pp. 85-88. Zbl0208.07503MR269783
- [4] G. Glaeser, Racine carrée d'une function differentiable, Ann. Inst. Fourier, 13 (1963), pp. 203-210. Zbl0128.27903MR163995
- [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. Zbl0312.35049MR427843
- [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. Zbl0505.35051MR653577
- [7] T. Nishitani, The Cauchy problem for weakly hyperbolic equations of second order, Comm. in Partial Diff. Equations, 5 (1980), pp. 1273-1296. Zbl0497.35053MR593968
- [8] O.A. Oleinik, On the Cauchy problem for weakly hyperbolic equations, Comm. Pure Appl. Math., 23 (1970), pp. 569-586. MR264227

## Citations in EuDML Documents

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- Massimo Cicognani, The geometric optics for a class of hyperbolic second order operators with Hölder continuous coefficients with respect to time
- F. Colombini, S. Spagnolo, Some examples of hyperbolic equations without local solvability
- Enrico Jannelli, Weakly hyperbolic equations of second order well-posed in some Gevrey classes
- Nicola Orrù, On a weakly hyperbolic equation with a term of order zero
- Enrico Jannelli, Weakly hyperbolic equations of second order well-posed in some Gevrey classes
- Alessia Ascanelli, Well posedness under Levi conditions for a degenerate second order Cauchy problem
- Robert Dalmasso, Un résultat sur les fonctions de classe ${C}^{1,\alpha}$ et application au problème de Cauchy
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