Parametric Borel summability for linear singularly perturbed Cauchy problems with linear fractional transforms
Publisher
Texas State University
Date
2019-04-29Funders
Ministerio de Economía y Competitividad
Bibliographic citation
Lastra, A. & Malek, S. 2019, “Parametric Borel summability for linear singularly perturbed Cauchy problems with linear fractional transforms”, Electronic Journal of Differential Equations, vol. 2019, no. 55, pp. 1-75
Keywords
Asymptotic expansion
Borel-Laplace transform
Cauchy problem
Difference equation
Integro-differential equation
Linear 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/publishedVersion
Publisher's version
https://ejde.math.txstate.eduRights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2019 Texas State University
Access rights
info:eu-repo/semantics/openAccess
Abstract
We consider a family of linear singularly perturbed Cauchy problems which combines partial differential operators and linear fractional transforms. This work is the sequel of a study initiated in [17]. We construct a collection of holomorphic solutions on a full covering by sectors of a neighborhood of the origin in C with respect to the perturbation parameter ϵ. This set is built up through classical and special Laplace transforms along piecewise linear paths of functions which possess exponential or super exponential growth/decay on horizontal strips. A fine structure which entails two levels of Gevrey asymptotics of order 1 and so-called order 1+ is presented. Furthermore, unicity properties regarding the 1+ asymptotic layer are observed and follow from results on summability with respect to a particular strongly regular sequence recently obtained in [13] .
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