ملخص: The aim of this work is the study of the Cauchy problem for a c of linear operators, non:necessarily kowalevskian, with shrinking argument. We prove the well posedness of this problem in the space of analytic functions with respect to time and Gevrey class with respect to spatial variable. Our tools are based on formal norms of Leray and Waelbroeck [J. Leray, L. Waelbroeck, Norme formelle d'une fonction composee (Preliminaire a l'etude des systemes non lineaires, hyperboliques non stricts), in: Colloque de Liege, CBRM, 1964, pp. 145:152. [23]], already used in [Cl. Wagschal, Le probleme de Goursat non lineaire, J. Math. Pure Appl. 58 (1979) 309:337; D. Gourdin, M. Mechab, Solution globale d'un probleme de Cauchy lineaire, J. Funct. Anal. 202 (2003) 123:146].

لغة: فرنسية