On parametric Gevrey asymptotics for initial value problems with infinite order irregular singularity and linear fractional transforms
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/41476DOI: 10.1186/s13662-018-1847-9
ISSN: 1687-1839
Publisher
Springer Open
Date
2018-10-23Funders
Ministerio de Economía y Competitividad
Bibliographic citation
Lastra, A. & Malek, S. 2018, “On parametric Gevrey asymptotics for initial value problems with infinite order irregular singularity and linear fractional transforms”, Advances in Difference Equations, vol. 2018, art. 386.
Keywords
Asymptotic expansion
Borel-Laplace transform
Fourier transform
Initial value problem
Difference equation
Formal power series
Nonlinear integro-differential equation
Nonlinear partial differential equation
Singular perturbation
Project
info:eu-repo/grantAgreement/MINECO//MTM2016-77642-C2-1-P/ES/Algebra y geometría en sistemas dinámicos y foliaciones singulares/
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/publishedVersion
Publisher's version
https://doi.org/10.1186/s13662-018-1847-9Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Access rights
info:eu-repo/semantics/openAccess
Abstract
This paper is a continuation of the work (Lastra and Malek in J. Differ. Equ. 259(10):5220-5270, 2015) where singularly perturbed nonlinear PDEs have been studied from an asymptotic point of view. Here, the partial differential operators are combined with particular Moebius transforms in the time variable. As a result, the leading term of the main problem needs to be regularized by means of a singularly perturbed infinite order formal irregular operator that allows us to construct a set of genuine solutions in the form of a Laplace transform in time and an inverse Fourier transform in space. Furthermore, we obtain Gevrey asymptotic expansions for these solutions of some order K > 1 in the perturbation parameter.
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