Sur les équations hyperboliques avec des coefficients qui ne dépendent que du temps

Ferruccio Colombini; Ennio De Giorgi; Sergio Spagnolo

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1979)

  • Volume: 6, Issue: 3, page 511-559
  • ISSN: 0391-173X

How to cite

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Colombini, Ferruccio, De Giorgi, Ennio, and Spagnolo, Sergio. "Sur les équations hyperboliques avec des coefficients qui ne dépendent que du temps." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 6.3 (1979): 511-559. <http://eudml.org/doc/83819>.

@article{Colombini1979,
author = {Colombini, Ferruccio, De Giorgi, Ennio, Spagnolo, Sergio},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {hyperbolic equation; existence and uniqueness; coercive equations; analytic solutions; Gevrey class; a priori estimates; perturbation},
language = {fre},
number = {3},
pages = {511-559},
publisher = {Scuola normale superiore},
title = {Sur les équations hyperboliques avec des coefficients qui ne dépendent que du temps},
url = {http://eudml.org/doc/83819},
volume = {6},
year = {1979},
}

TY - JOUR
AU - Colombini, Ferruccio
AU - De Giorgi, Ennio
AU - Spagnolo, Sergio
TI - Sur les équations hyperboliques avec des coefficients qui ne dépendent que du temps
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1979
PB - Scuola normale superiore
VL - 6
IS - 3
SP - 511
EP - 559
LA - fre
KW - hyperbolic equation; existence and uniqueness; coercive equations; analytic solutions; Gevrey class; a priori estimates; perturbation
UR - http://eudml.org/doc/83819
ER -

References

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  1. [1] F. Colombini - S. Spagnolo, On the convergence of solutions of hyperbolic equations, Comm. Partial Differential Equations, 3 (1978), pp. 77-103. Zbl0375.35034MR493117
  2. [2] L. De Simon - G. Torelli, Linear second order differential equations with discontinuous coefficients in Hilbert spaces, Ann. Scuola Norm. Sup. Pisa, 1 (1974), pp. 131-154. Zbl0318.35055MR388168
  3. [3] J.M. Gelfand - G.E. Shilov, Generalized functions, vol. II et III, Academic Press, New York, 1967 (édition originelle: Moscou, 1958). Zbl0355.46017
  4. [4] A.E. Hurd - D.H. Sattinger, Questions of existence and uniqueness for hyperbolic equations with discontinuous coefficients, Trans. Amer. Math. Soc., 132 (1968), pp. 159-174. Zbl0155.16401MR222457
  5. [5] J.L. Lions, Equations différentielles opérationnelles et problèmes aux limites, Springer, Berlin, 1961. Zbl0098.31101MR153974
  6. [6] J.L. Lions - E. Magenes, Problèmes aux limites non homogènes et applications, Dunod, Paris, 1968. Zbl0165.10801
  7. [7] A. Martineau, Sur les fonctionnelles analytiques et la transformation de Fourier-Borel,J. Analyse Math., 11 (1963), pp. 1-164. Zbl0124.31804MR159220
  8. [8] W.T. Reid, On the approximation of integrable functions by functions of bounded variation, Ann. Scuola Norm. Sup. Pisa, 14 (1960), pp. 133-140. Zbl0097.27503MR126514
  9. [9] C. Roumieu, Sur quelques extensions de la notion de distributions, Ann. Sci. École Norm. Sup., 77 (1960), pp. 47-121. Zbl0104.33403MR121643
  10. [10] C. Roumieu, Ultradistributions définies sur Rn et sur certaines classes de variétés différentiables, J. Analyse Math., 10 (1962-63), pp. 153-192. Zbl0122.34802MR158261
  11. [11] F. Treves, Basic linear partial differential equations, Academic Press, New York, 1975. Zbl0305.35001MR447753

Citations in EuDML Documents

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  1. Ferruccio Colombini, Quelques résultats de non résolubilité locale pour des équations hyperboliques
  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. Ferruccio Colombini, Daniele del Santo, Tamotu Kinoshita, Well-posedness of the Cauchy problem for a hyperbolic equation with non-Lipschitz coefficients
  4. Ferruccio Colombini, Guy Métivier, The Cauchy problem for wave equations with non Lipschitz coefficients; Application to continuation of solutions of some nonlinear wave equations
  5. Massimo Cicognani, The geometric optics for a class of hyperbolic second order operators with Hölder continuous coefficients with respect to time
  6. F. Colombini, S. Spagnolo, Some examples of hyperbolic equations without local solvability
  7. F. Colombini, E. Jannelli, S. Spagnolo, Well-posedness in the Gevrey classes of the Cauchy problem for a non-strictly hyperbolic equation with coefficients depending on time
  8. Marina Ghisi, Analytic solutions to nonlocal abstract equations
  9. Enrico Jannelli, Weakly hyperbolic equations of second order well-posed in some Gevrey classes
  10. Nicola Orrù, On a weakly hyperbolic equation with a term of order zero

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