On the radius of spatial analyticity for semilinear symmetric hyperbolic systems

We study the problem of propagation of analytic regularity for semi-linear symmetric hyperbolic systems. We adopt a global perspective and we prove that if the initial datum extends to a holomorphic function in a strip of radius (=width) \epsilon_0, the same happens for the solution u(t,.) for a certain radius \epsilon(t), as long as the solution exists. Our focus is on precise lower bounds on the spatial radius of analyticity \epsilon(t) as t grows. We also get similar results for the Schroedinger equation with a real-analytic electromagnetic potential.