Parametric Gevrey asymptotics in two complex time variables through truncated Laplace transforms
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/44947DOI: 10.1186/s13662-020-02773-z
ISSN: 1687-1839
Publisher
SpringerOpen
Date
2020-06-19Funders
Ministerio de Economía y Competitividad
Universidad de Alcalá
Bibliographic citation
Chen, G., Lastra, A. & Malek, S. Parametric Gevrey asymptotics in two complex time variables through truncated Laplace transforms. Adv Differ Equ 2020, 307 (2020).
Keywords
Asymptotic expansion
Borel-Laplace transform
Fourier transform
Initial value problem
Formal power series
Nonlinear 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/
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/s13662-020-02773-zRights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Access rights
info:eu-repo/semantics/openAccess
Abstract
This work is devoted to the study of a family of linear initial value problems of partial differential equations in the complex domain, dealing with two complex time variables. The use of a truncated Laplace-like transformation in the construction of the analytic solution allows one to overcome a small divisor phenomenon arising from the geometry of the problem and represents an alternative approach to the one proposed in a recent work (Lastra and Malek in Adv. Differ. Equ. 2020:20, 2020) by the last two authors. The result leans on the application of a fixed point argument and the classical Ramis-Sibuya theorem.
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