Local solution of Cauchy problem for nonlinear hyperbolic systems in Gevrey classes

Abstract

0. 4) |D_{x}^{\alpha}D_{y}^{\beta}F_{i}(x, y)|\leq CA^{|\alpha|+1\beta|}|\alpha|!^{s}|\beta|! , x in \Omega , y in V , for \alpha\in N^{n\dagger 1} , \beta\in N^{r} .