On a q-analog of a singularly perturbed problem of irregular type with two complex time variables

Authors
Lastra Sedano, AlbertoUniversity of Alcalá Author; Malek, Stephane
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/41509
DOI: 10.3390/math7100924
ISSN: 2227-7390
Publisher
MDPI
Date
2019-10-03
Affiliation
Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
Funders
Ministerio de Economía y Competitividad
Bibliographic citation
Lastra, A. & Malek, S. 2019, “On a q-analog of a singularly perturbed problem of irregular type with two complex time variables”, Mathematics, vol. 7, no. 10, 924
Keywords
Asymptotic expansion
Borel-Laplace transform
Fourier transform
Initial value problem
Formal power series
q-difference equation
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/
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/publishedVersion
Publisher's version
https://doi.org/10.3390/math7100924
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Access rights
info:eu-repo/semantics/openAccess
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Abstract
The analytic solutions of a family of singularly perturbed q-difference-differential equations in the complex domain are constructed and studied from an asymptotic point of view with respect to the perturbation parameter. Two types of holomorphic solutions, the so-called inner and outer solutions, are considered. Each of them holds a particular asymptotic relation with the formal ones in terms of asymptotic expansions in the perturbation parameter. The growth rate in the asymptotics leans on the --1-branch of Lambert W function, which turns out to be crucial.
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