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 Schrodinger equation with a real-analytic electromagnetic potential. (C) 2014 Elsevier Inc. All rights reserved