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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


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.

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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.

© 2002  Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. All Rights Reserved.
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