Abstract
We study the linear Cauchy problem for partial differential equations of Fuchs type. We prove the global existence and uniqueness of a solution to this problem in the space of sufficiently differentiable functions with respect to the Fuchsian variable and in Gevrey spaces with respect to the other variables. The method of proof is based on the application of the fixed point theorem in some Banach spaces defined by majorant functions that are suitable to this kind of equations.
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