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A Fuchs-type Cauchy problem in Gevrey spaces. (Problème de Cauchy Fuchsien dans les Espaces de Gevrey.) (French. English summary) Zbl 1064.35039
Summary: The authors study in this article the Cauchy problem for partial differential equations of Fuchs type in the space of holomorphic functions with respect to the Fuchsian variable and in Gevrey spaces with respect other variables. The results are in some sense a generalization of those obtained in P. Pongérard and C. Wagschal [J. Math. Pures Appl., IX. Sér. 75, 409–418 (1996; Zbl 0858.35001)] for the non characteristic Cauchy problem in the space of entire functions and in P. Pongérard [J. Math. Sci., Tokyo 8, 89–105 (2001; Zbl 0984.35004)] in the case of Fuchsian operators.

35G10 Initial value problems for linear higher-order PDEs
35C10 Series solutions to PDEs
35A20 Analyticity in context of PDEs