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.
On the radius of spatial analyticity for semilinear symmetric hyperbolic systems / D'Ancona, Piero Antonio; F., Nicola; M., Cappiello. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 256:7(2014), pp. 2603-2618. [10.1016/j.jde.2014.01.020]
On the radius of spatial analyticity for semilinear symmetric hyperbolic systems
D'ANCONA, Piero Antonio;
2014
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
