Skip to main content
Log in

Propagation de l'analyticité des solutions de systèmes hyperboliques non-linéaires

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Bibliographie

  1. Baouendi, M.S., Goulaouic, C.: Cauchy problems for analytic pseudodifferential operators. Comm. in Partial Differential Equations1, 135–189 (1976)

    Google Scholar 

  2. Baouendi, M.S., Goulaouic, C.: Remarks on the abstract form of non linear Cauchy Kovalevsky theorems. Comm. in Partial Differential Equations2, 1151–1162 (1977)

    Google Scholar 

  3. Bardos, C.: Analyticité de la solution de l'équation d'Euler dans un ouvert de ℝn. C.R. Acad. Sc. Parist 283, 255–258 (1976)

    Google Scholar 

  4. Bardos, C., Benachour, S., Zerner, M.: Analytiticité des solutions périodiques de l'équation d'Euler en dimension deux. C.R. Acad. Sc. Parist 282, 995–998 (1976)

    Google Scholar 

  5. Benachour, S.: Analyticité des solutions périodiques de l'équation d'Euler en dimension trois. C.R. Acad. Sc. Parist 283, 107–110 (1976)

    Google Scholar 

  6. Bernstein, S.: Démonstration du théorème de M. Hilbert sur la nature analytique des solutions des équations de type elliptique Math. Z.28, 330–348 (1928)

    Google Scholar 

  7. Bony, J.M.: Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires. Ann. Scient. E.N.S., 4éme série14, 209–246 (1981)

    Google Scholar 

  8. Bony, J.M.: Interaction des singularités pour les équations aux dérivées partielles non linéaires; Séminaire Goulaouic-Meyer-Schwartz, Année 1981–82-Ecole Polytechnique, Paris

  9. Friedman, A.: On the regularity of the solutions of non linear elliptic and parabolic systems of partial differential equations. J. Math. Mech.7, 43–60 (1958)

    Google Scholar 

  10. Friedrichs, K.O.: Symetric hyperbolic linear differential equations. Comm. Pure Appl. Math.7, 345–392 (1954)

    Google Scholar 

  11. Hörmander, L.: Linear partial differential operators. Berlin-Heidelberg-New York: Springer 1969

    Google Scholar 

  12. Hörmander, L.: Uniqueness theorem and wave front sets for solutions of linear differential equations with analytic coefficients. Comm. Pure Appl. Math.24, 671–704 (1971)

    Google Scholar 

  13. Bros, J., Iagolnitzer, D.: Support essentiel et structure analytique des distributions; Séminaire Goulaouic-Lions-Schwartz, Année 1974–75, Ecole Polytechnique, Paris

  14. Lascar, B.: Singularité des solutions d'équations aux dérivées partielles non linéaires. C.R. Acad. Sc. Parist 287, 527–529 (1978)

    Google Scholar 

  15. Lax, P.D.: Non linear hyperbolic equations. Comm. on Pure Appl. Math.6, 231–258 (1953)

    Google Scholar 

  16. Mizohata, S.: Analyticity of solutions of hyperbolic systems with analytic coefficients. Comm. Pure Appl. Math.14, 547–559 (1961)

    Google Scholar 

  17. Morrey, C.B.: Multiple integrals in the calculs of variations. Berlin-Heidelberg-New York: Springer 1966

    Google Scholar 

  18. Nirenberg, L.: Pseudodifferential operators. Proc. Sympos. Pure Math., vol. 16. Amer. Math. Soc., Providence R.I. 149–167 (1970)

    Google Scholar 

  19. Nirenberg, L.: An abstract from of the non linear Cauchy-Kovalevsky theorem. J. Diff. Geometry6, 561–576 (1972)

    Google Scholar 

  20. Nishida, T.: A note on the Nirenberg's theorem as an abstract form of the non linear Cauchy-Kovalevsky theorem in a scale of Banach spaces. J. Diff. Geometry12, 629–633 (1977)

    Google Scholar 

  21. Ovsjannikov, L.V.: A non linear Cauchy problem in a scale of Banach spaces. Dok. Akad. Nauk SSRR200 (1971); Sov. Math. Dokl12, 1497–1502 (1971)

    Google Scholar 

  22. Petrowsky, I.: Sur l'analyticité des solutions des systèmes d'équations différentielles. Ree. Math. N.S. Math. Sbornik5, (47) 3–70 (1939)

    Google Scholar 

  23. Rauch, J.: Singularities of solutions to semi-linear wave equations. J. Math. Pure Appl.58, 299–308 (1979)

    Google Scholar 

  24. Sato, M.: Hyperfunctions and partial differential equations. Proc. Int. Conf. Funct. Anal. Tokyo 91–94 (1969)

  25. Taylor, M.E.: Pseudodifferential operators; Princeton Mathematical Series, no 34, Princeton University Press

  26. Wagschall, C.: Le problème de Goursat non linéaire, Séminaire Goulaouic-Schwartz, Année 1978–79, Ecole Polytechnique, Paris

Download references

Author information

Authors and Affiliations

Authors

Additional information

A la mémoire de C. Goulaouic

Note. C. Goulaouic nous a informé qu'il a obtenu une preuve différente (en cours de rédaction) de certains résultats présentés ici, preuve qui utilise une continuation dans le domaine complexe

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alinhac, S., Metivier, G. Propagation de l'analyticité des solutions de systèmes hyperboliques non-linéaires. Invent Math 75, 189–204 (1984). https://doi.org/10.1007/BF01388563

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01388563

Navigation