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2014 On Parametric Gevrey Asymptotics for Some Cauchy Problems in Quasiperiodic Function Spaces
A. Lastra, S. Malek
Abstr. Appl. Anal. 2014: 1-29 (2014). DOI: 10.1155/2014/153169

Abstract

We investigate Gevrey asymptotics for solutions to nonlinear parameter depending Cauchy problems with 2π-periodic coefficients, for initial data living in a space of quasiperiodic functions. By means of the Borel-Laplace summation procedure, we construct sectorial holomorphic solutions which are shown to share the same formal power series as asymptotic expansion in the perturbation parameter. We observe a small divisor phenomenon which emerges from the quasiperiodic nature of the solutions space and which is the origin of the Gevrey type divergence of this formal series. Our result rests on the classical Ramis-Sibuya theorem which asks to prove that the difference of any two neighboring constructed solutions satisfies some exponential decay. This is done by an asymptotic study of a Dirichlet-like series whose exponents are positive real numbers which accumulate to the origin.

Citation

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A. Lastra. S. Malek. "On Parametric Gevrey Asymptotics for Some Cauchy Problems in Quasiperiodic Function Spaces." Abstr. Appl. Anal. 2014 1 - 29, 2014. https://doi.org/10.1155/2014/153169

Information

Published: 2014
First available in Project Euclid: 27 February 2015

zbMATH: 07021820
MathSciNet: MR3294868
Digital Object Identifier: 10.1155/2014/153169

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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