On parametric Gevrey asymptotics for some initial value problems in two asymmetric complex time variables
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/41474DOI: 10.1007/s00025-018-0914-6
ISSN: 1422-6383
Publisher
Springer Verlag
Date
2018-11-01Funders
Ministerio de Economía y Competitividad
Bibliographic citation
Lastra, A. & Malek, S. 2018, “On parametric Gevrey asymptotics for some initial value problems in two asymmetric complex time variables”, Results in Mathematics, vol. 73, article 155
Keywords
Asymptotic expansion
Borel-Laplace transform
Fourier transform
Initial value problem
Formal power series
Nonlinear integro-differential equation
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/
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
https://doi.org/10.1007/s00025-018-0914-6Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2018 Springer Verlag
Access rights
info:eu-repo/semantics/openAccess
Abstract
We study a family of nonlinear initial value problem for partial differential equations in the complex domain under the action of two asymmetric time variables. Different Gevrey bounds and multisummability results are obtained depending on each element of the family, providing a more complete picture on the asymptotic behavior of the solutions of PDEs in the complex domain in several complex variables.
The main results lean on a fixed point argument in certain Banach space in the Borel plane, together
with a Borel summability procedure and the action of different Ramis-Sibuya type theorems.
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