Global solutions of the nonlinear Goursat problem in Gevrey classes (Q1358680)

The authors investigate the Goursat problem with zero data for equations of type \[ D^\alpha_x u(x,y)= \Phi\Biggl(x,y,D^B u(x,y), \int [D^B u(x,y)]^2 dy\Biggr), \] generalized Kirchhoff type equations. When \(\Phi(x,y,z,\tau)\) is a polynomial with respect to the variable \(y\), one establishes the existence of a global solution in the space of functions which are holomorphic with respect to the variable \(x\) and in the Gevrey class with respect to the variable \(y\).