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Systèmes Linéaires, Hyperboliques Non-Stricts

In: Hyperbolic Equations and Waves

Author

Listed:
  • J. Leray
  • Y. Ohya

Abstract

Résumé Les systèmes strictement hyperboliques se résolvent dans des espaces de fonctions ayant un nombre donné, fini, de dérivées (Petrowsky[10] Leray [5][6], Gärding [1]). Une équation à caractéristiques multiples ne peut plus être résolue dans de tels espaces (Yamaguti [12]; Mme Lax Hörmander [3], ch. V, qui réserve le terme « hyperbolique » au strictement hyperbolique). Mais eile peut l’être dans des espaces de fonctions indéfiniment différentiables: les classes de Gevrey γ(α) (Hörmander [3], théorème 5.7.3, traite l’équation linéaire à coefficients constants; Ohya [9] traite l’équation linéaire à coefficients variables, dont le polynôme caractéristique est un produit de polynômes strictement hyperboliques; le domaine d’influence existe. Ce domaine peut s’étudier comme dans le cas strictement hyperbolique, [5], ch VI).

Suggested Citation

  • J. Leray & Y. Ohya, 1970. "Systèmes Linéaires, Hyperboliques Non-Stricts," Springer Books, in: M. Froissart (ed.), Hyperbolic Equations and Waves, pages 283-322, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-87025-5_22
    DOI: 10.1007/978-3-642-87025-5_22
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