Working Paper Article Version 1 This version is not peer-reviewed

# Some Notes on the Parametric Gevrey Asymptotics in Two Complex Time Variables Through Truncated Laplace Transforms

Version 1 : Received: 29 September 2020 / Approved: 30 September 2020 / Online: 30 September 2020 (13:06:44 CEST)

How to cite: Chen, G.; Lastra, A.; Malek, S. Some Notes on the Parametric Gevrey Asymptotics in Two Complex Time Variables Through Truncated Laplace Transforms. Preprints 2020, 2020090746 Chen, G.; Lastra, A.; Malek, S. Some Notes on the Parametric Gevrey Asymptotics in Two Complex Time Variables Through Truncated Laplace Transforms. Preprints 2020, 2020090746

## Abstract

This paper is a slightly modified, abridged version of a previous work Parametric Gevrey asymptotics in two complex time variables through truncated Laplace transforms'' motivated by our contribution in the conference Formal and Analytic Solutions of Diff. (differential, partial differential, difference, q-difference, q-difference-differential) Equations on the Internet'' (FASnet20). It aims to clarify and give further detail at some crucial points concerning the asymptotic behavior of the solutions of the problems studied in that work.

## Subject Areas

Asymptotic expansion; Borel-Laplace transform; Fourier transform; initial value problem; formal power series; linear partial differential equation; singular perturbation

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