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Comptes Rendus Mathématique
Volume 339, n° 10
pages 695-698 (novembre 2004)
Doi : 10.1016/j.crma.2004.09.034
Received : 13 January 2004 ;  accepted : 21 September 2004
Sur un théorème de Cauchy-Kowalewski-Nagumo global dans des espaces de Gevrey projectifs
On a global Cauchy-Kowalewski-Nagumo theorem in projective Gevrey space.
 

Daniel Gourdin a , Todor Gramchev b
a UFR 920, université de Paris 6, 4, place Jussieu, 75252 Paris cedex 05, France 
b Dipartimento Matematica, Università di Cagliari, via Ospedale, 72, 09124 Calgliari, Italie 

Résumé

Nous proposons une nouvelle approche, basée à la fois sur le principe de contraction et celui des approximations successives de Picard, pour lʼétude dʼun problème de Cauchy global associé à lʼopérateur aux dérivées partielles   à coefficients   continus ou holomorphes en t dans les espaces de Gevrey projectifs. Nous généralisons aussi les résultats dʼune Note précédente au cas dʼopérateurs non Kowalewskiens. Pour citer cet article : D. Gourdin, T. Gramchev, C. R. Acad. Sci. Paris, Ser. I 339 (2004).

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Abstract

We propose a new approach, based on a combination of the contraction principle and Picard successive approximations, for the study of a global Cauchy problem associated to partial differential operator   with coefficients   continuous or holomorphic with respect to t in projective Gevrey spaces. We extend the result of a previous Note to the case of non Kowalewskian operators. To cite this article: D. Gourdin, T. Gramchev, C. R. Acad. Sci. Paris, Ser. I 339 (2004).

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