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Norme Formelle d’une Fonction Composée (Préliminaire a l’Étude des Systèmes Non-Linéaires, Hyperboliques Non-Stricts)

In: Hyperbolic Equations and Waves

Author

Listed:
  • J. Leray
  • L. Waelbroeck

Abstract

Résumé J. Leray et Y. Ohya [4], en employant une suggestion de L. Waelbroeck, ont étudié les systèmes hyperboliques non stricts, dans le cas linéaire. Cette méthode s’adapte au cas non linéaire: on opère [5] par approximations successives, comme le fait P. Dionne [2] dans le cas strictement hyperbolique, mais en remplaçant les espaces de Sobolev par des classes de Gevrey, les normes de Sobolev par des normes formelles; la majoration de ces approximations successives résulte de la résolution d’un problème de Cauchy formel, non linéaire, qu’on ramène au problème de Cauchy-Kowalewski (1) par des opérateurs transformant les classes de Gevrey formelles en classes de fonctions holomorphes.

Suggested Citation

  • J. Leray & L. Waelbroeck, 1970. "Norme Formelle d’une Fonction Composée (Préliminaire a l’Étude des Systèmes Non-Linéaires, Hyperboliques Non-Stricts)," Springer Books, in: M. Froissart (ed.), Hyperbolic Equations and Waves, pages 323-330, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-87025-5_23
    DOI: 10.1007/978-3-642-87025-5_23
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