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Comptes Rendus Mathématique
Volume 334, n° 7
pages 563-567 (2002)
Doi : S1631-073X(02)02272-0
Received : 23 April 2001 ; 
Sur un théorème de Cauchy-Kowalewski-Nagumo global
On a global Cauchy-Kowalewski-Nagumo theorem
 

Daniel Gourdin a , Mustapha Mechab b
a UFR 920, Université Paris 6, 4, place Jussieu, 75252 Paris cedex 05, France 
b Laboratoire de mathématiques, Université Djilali Liabès, BP 89, 22000 Sidi Bel Abbès, Algérie 

Note présentée par Yvonne Choquet-Bruhat

Résumé

Dans cette Note, on établit des résultats d'existence et d'unicité de la solution de certains problèmes de Cauchy linéaires. Dans le cas holomorphe, notre résultat précise les résultats de [4] et les étend au cas des conditions initiales de classes Gevrey. Dans le cas continu, c'est une généralisation du théorème de N. Nagumo et une extension des résultats de [5] et [1] au cas des conditions initiales de classes Gevrey, sans la condition d'hyperbolicité. Pour citer cet article : D. Gourdin, M. Mechab, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 563-567.

The full text of this article is available in PDF format.
Abstract

In this Note, we solve some global linear Cauchy problems. In the holomorphic case, for some operators, our result extends those of [4] when the initial data is in Gevrey class. In the continuous case, we give a generalisation of the local result of N. Nagumo, and on other hand, our result is an extension of the results of [5,1] for Gevrey initial data without the hyperbolicity condition. To cite this article: D. Gourdin, M. Mechab, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 563-567.

The full text of this article is available in PDF format.


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