GLOBAL SOLUTIONS OF THE FUCHSIAN-CAUCHY PROBLEM IN GEVREY SPACES

Abstract

We consider the Fuchsian Cauchy problem associated to linear partial differential equations with Fuchsian principal part of order m and weight μ in the sense of M. S. Baouendi and C. Goulaouic [2]. We obtain existence and uniqueness of a global solution to this problem in the space of holomorphic functions with respect to the fuchsian variable t and in Gevrey spaces with respect to the other variable x. The method of proof is based on the application of the fixed point theorem in some Banach spaces defined by majorant functions that are suitables to this kind of equations. We introduce new majorant functions as in [4]and [5] which allow us to simplify the proof given in [3].