On singularly perturbed linear initial value problems with mixed irregular and Fuchsian time singularities
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/41533DOI: 10.1007/s12220-019-00221-3
ISSN: 1050-6926
Publisher
Springer Verlag
Date
2019-06-13Embargo end date
2020-06-13Funders
Ministerio de Economía y Competitividad
Bibliographic citation
Lastra, A. & Malek, S. 2019, “On singularly perturbed linear initial value problems with mixed irregular and Fuchsian time singularities”, Journal of Geometric Analysis (2019)
Keywords
Asymptotic expansion
Borel-Laplace transform
Fourier transform
Initial value problem
Formal power series
Linear integro-differential equation
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/acceptedVersion
Publisher's version
https://doi.org/10.1007/s12220-019-00221-3Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2019 Springer Verlag
Access rights
info:eu-repo/semantics/openAccess
Abstract
We consider a family of linear singularly perturbed PDE depending on a complex perturbation parameter ϵ. As in the former study (Lastra and Malek in J Differ Equ 259(10):5220-5270, 2015) of the authors, our problem possesses an irregular singularity in time located at the origin but, in the present work, it also entangles differential operators of Fuchsian type acting on the time variable. As a new feature, a set of sectorial holomorphic solutions are built up through iterated Laplace transforms and Fourier inverse integrals following a classical multisummability procedure introduced by W. Balser. This construction has a direct consequence on the Gevrey bounds of their asymptotic expansions w.r.t ϵ which are shown to increase the order of the leading term which combines both irregular and Fuchsian types operators.
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