Local solution of Cauchy problem for nonlinear hyperbolic systems in Gevrey classes
Local solution of Cauchy problem for nonlinear hyperbolic systems in Gevrey classes
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} .We define the characteristic matrix for \{F_{i}\} as follows p_{ij}(x, y, \xi)=\sum_{\alpha\in M_{ij}}(\partial/\partial y_{\alpha})F_{i}(x, y)\xi^{\alpha}|\alpha|=m+n_{j}-n_{i} ' i,j=1 , \cdots , N' .which is a polynomial in \xi of degree m+n_{j}-n_{i} …