CAUCHY PROBLEM IN INHOMOGENEOUS GEVREY CLASSES

In this work we study the well-posedness of the Cauchy Problem for weakly hyperbolic systems in inhomogeneous Gevrey classes, that extend the standard Gevrey functions. Particular cases are represented by anysotropic Gevrey classes and generalized Gevrey classes defined in terms of a complete polyhedron. Well-posedness is obtained by imposing some restrictions on the lower order terms, depending on the Gevrey class and on the order of the operator. The main tools of the proof are the technique of quasi-symmetrization and approximated energy estimates.