On the radius of spatial analyticity for semilinear symmetric hyperbolic systems

Marco Cappiello; Piero D'Ancona; Fabio Nicola

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arXiv · 1309.1281

On the radius of spatial analyticity for semilinear symmetric hyperbolic systems

Marco Cappiello·Piero D'Ancona·Fabio Nicola

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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) ε_0, the same happens for the solution u(t,.) for a certain radius ε(t), as long as the solution exists. Our focus is on precise lower bounds on the spatial radius of analyticity ε(t) as t grows. We also get similar results for the Schroedinger equation with a real-analytic electromagnetic potential.

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Marco Cappiello, Piero D'Ancona, Fabio Nicola. 2013-09-05. On the radius of spatial analyticity for semilinear symmetric hyperbolic systems. https://arxiv.org/abs/1309.1281

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