Global analytic solutions to hyperbolic systems (Q1386401)

For weakly hyperbolic \(N\times N\)-systems of the type \[ u_t- \sum^n_{j= 1}A_j\Biggl( \int_\Omega u^2_1dx,\dots, \int_\Omega u^2_Ndx\Biggr) u_{x_j}= 0, \] with real-valued, continuous, bounded \(N\times N\)-matrices \(A_j\), the periodic initial-boundary value problem for \(\Omega= (0,2\pi)^n\) is considered, and the global well-posedness in the analytic class is proved. For \(2\times 2\)-systems in one space dimension, the boundedness assumption on the coefficients can be replaced by another set of conditions. Remarks on the Cauchy problem in \(\Omega= \mathbb{R}^n\) are also included.