Strongly regular multi-level solutions of singularly perturbed linear partial differential equations

Authors
Lastra Sedano, AlbertoUniversity of Alcalá Author; Malek, Stephane; Sanz, Javier
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/41438
DOI: 10.1007/s00025-015-0493-8
ISSN: 1422-6383
Publisher
Springer Verlag
Date
2016-11-01
Affiliation
Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
Funders
Ministerio de Economía y Competitividad
Bibliographic citation
Lastra, A., Malek, S. & Sanz, J. 2016, “Strongly regular multi-level solutions of singularly perturbed linear partial differential equations”, Results in Mathematics, 2016, vol. 70, pp. 581-614.
Keywords
Linear partial differential equations
Singular perturbations
Formal power series
Borel-Laplace transform
Borel summability
Gevrey asymptotic expansions
Strongly regular sequence
Project
info:eu-repo/grantAgreement/MINECO//MTM2012-31439/ES/ANALISIS DE PERTURBACIONES SINGULARES: ESTUDIO ASINTOTICO, CAPAS LIMITE Y FENOMENOS MULTIESCALA/
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
https://doi.org/10.1007/s00025-015-0493-8
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2016 Springer Verlag
Access rights
info:eu-repo/semantics/openAccess
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Abstract
We study the asymptotic behavior of the solutions related to a family of singularly perturbed partial differential equations in the complex domain. The analytic solutions are asymptotically represented by a formal power series in the perturbation parameter. The geometry of the problem and the nature of the elements involved in it give rise to different asymptotic levels related to the so-called strongly regular sequences. The result leans on a novel version of amulti-level Ramis-Sibuya theorem.
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