On multiscale Gevrey and q-Gevrey asymptotics for some linear q-difference-differential initial value Cauchy problems

Authors
Lastra Sedano, AlbertoUniversity of Alcalá Author; Malek, Stephane
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/41440
DOI: 10.1080/10236198.2017.1337104
ISSN: 1023-6198
Publisher
Taylor & Francis
Date
2017-06-12
Affiliation
Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
Bibliographic citation
Lastra, A. & Malek, S. 2017, “On multiscale Gevrey and q-Gevrey asymptotics for some linear q-difference differential initial value Cauchy problems”, Journal of Difference Equations and Applications, vol. 23, no. 8, pp. 1397-1457
Keywords
Asymptotic expansion
Borel-Laplace transform
Fourier transform
Cauchy problem
Formal power series
Nonlinear integro-differential equation
Nonlinear partial differential equation
Singular perturbation
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
https://doi.org/10.1080/10236198.2017.1337104
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2017 Taylor & Francis
Access rights
info:eu-repo/semantics/openAccess
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Abstract
We study the asymptotic behavior of the solutions related to a singularly perturbed q-difference-differential problem in the complex domain. The analytic solution can be splitted according to the nature of the equation and its geometry so that both, Gevrey and q-Gevrey asymptotic phenomena are observed and can be distinguished, relating the analytic and the formal solution. The proof leans on a two level novel version of Ramis-Sibuya theorem under Gevrey and q-Gevrey orders.
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