Version 1
: Received: 14 June 2022 / Approved: 15 June 2022 / Online: 15 June 2022 (10:36:54 CEST)
Version 2
: Received: 14 September 2022 / Approved: 15 September 2022 / Online: 15 September 2022 (02:00:35 CEST)
Malek, S. Small Divisors Effects in Some Singularly Perturbed Initial Value Problem with Irregular Singularity. Analysis 2022, 0, doi:10.1515/anly-2022-1077.
Malek, S. Small Divisors Effects in Some Singularly Perturbed Initial Value Problem with Irregular Singularity. Analysis 2022, 0, doi:10.1515/anly-2022-1077.
Malek, S. Small Divisors Effects in Some Singularly Perturbed Initial Value Problem with Irregular Singularity. Analysis 2022, 0, doi:10.1515/anly-2022-1077.
Malek, S. Small Divisors Effects in Some Singularly Perturbed Initial Value Problem with Irregular Singularity. Analysis 2022, 0, doi:10.1515/anly-2022-1077.
Abstract
We examine a nonlinear initial value problem both singularly perturbed in a complex parameter and singular in complex time at the origin. The study undertaken in this paper is the continuation of a joined work with A. Lastra published in 2015. A change of balance between the leading and a critical subdominant term of the problem considered in our previous work is performed. It leads to a phenomenon of coalescing singularities to the origin in the Borel plane w.r.t time for a finite set of holomorphic solutions constructed as Fourier series in space on horizontal complex strips. In comparison to our former study, an enlargement of the Gevrey order of the asymptotic expansion for these solutions relatively to the complex parameter is induced.
Keywords
asymptotic expansion; Borel-Laplace transform; Fourier series; initial value problem; formal power series; singular perturbation
Subject
Computer Science and Mathematics, Analysis
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
