Boundary layer expansions for initial value problems with two complex time variables

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Authors
Lastra Sedano, AlbertoUniversity of Alcalá Author; Malek, Stephane
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/41482
DOI: 10.1186/s13662-020-2496-3
ISSN: 1687-1839
Publisher
SpringerOpen
Date
2020-01-09
Academic Departments
Universidad de Alcalá. Departamento de Física y Matemáticas
Teaching unit
Unidad Docente Matemáticas
Funders
Ministerio de Economía y Competitividad
Universidad de Alcalá
Bibliographic citation
Lastra, A. & Malek, S. 2020, “Boundary layer expansions for initial value problems with two complex time variables”, Advances in Difference Equations, vol. 2020, article 20
Keywords
Asymptotic expansion
Borel-Laplace transform
Fourier transform
Initial value problem
Formal power series
Boundary layer
Singular perturbation
Project
info:eu-repo/grantAgreement/MINECO//MTM2016-77642-C2-1-P/ES/Algebra y geometría en sistemas dinámicos y foliaciones singulares/
info:eu-repo/grantAgreement/UAH//CM-JIN-2019-010
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/publishedVersion
Publisher's version
https://doi.org/10.1186/s13662-020-2496-3
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Access rights
info:eu-repo/semantics/openAccess
Abstract
We study a family of partial differential equations in the complex domain, under the action of a complex perturbation parameter ϵ. We construct inner and outer solutions of the problem and relate them to asymptotic representations via Gevrey asymptotic expansions with respect to ϵ in adequate domains. The asymptotic representation leans on the cohomological approach determined by the Ramis-Sibuya theorem.

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