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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Colombini, 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

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  1. [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. [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. [3] J. Dieudonné, Sur un théorème de Glaeser, J. Analyse Math., 23 (1970), pp. 85-88. Zbl0208.07503MR269783
  4. [4] G. Glaeser, Racine carrée d'une function differentiable, Ann. Inst. Fourier, 13 (1963), pp. 203-210. Zbl0128.27903MR163995
  5. [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. [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. [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. [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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  1. Kunihiko Kajitani, Yasuo Yuzawa, The Cauchy problem for hyperbolic systems with Hölder continuous coefficients with respect to the time variable
  2. Tamotu Kinoshita, On the wellposedness in the Gevrey classes of the Cauchy problem for weakly hyperbolic equations whose coefficients are Hölder continuous in t and degenerate in t = T
  3. Massimo Cicognani, The geometric optics for a class of hyperbolic second order operators with Hölder continuous coefficients with respect to time
  4. F. Colombini, S. Spagnolo, Some examples of hyperbolic equations without local solvability
  5. Enrico Jannelli, Weakly hyperbolic equations of second order well-posed in some Gevrey classes
  6. Nicola Orrù, On a weakly hyperbolic equation with a term of order zero
  7. Enrico Jannelli, Weakly hyperbolic equations of second order well-posed in some Gevrey classes
  8. Alessia Ascanelli, Well posedness under Levi conditions for a degenerate second order Cauchy problem
  9. Robert Dalmasso, Un résultat sur les fonctions de classe C 1 , α et application au problème de Cauchy
  10. Tatsuo Nishitani, Sergio Spagnolo, On pseudosymmetric systems with one space variable

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