On the radius of spatial analyticity for semilinear symmetric hyperbolic systems

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:256

Article

Cappiello, Marco¹  D'Ancona, Piero²  Nicola, Fabio³ 

[1] Univ Turin, Dipartimento Matemat, I-10123 Turin, Italy

[2] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy

[3] Politecn Torino, Dipartimento Sci Matemat, I-10129 Turin, Italy

关键词: Hyperbolic systems;    Holomorphic extension;    Radius of analyticity;   

DOI  :  10.1016/j.jde.2014.01.020

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free