On parametric Gevrey asymptotics for singularly perturbed partial differential equations with delays

2013/07/17 by Alberto Lastra, Lastra, Alberto, Stéphane Malek +1
Mathematics · #35C10 #35C20 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Equations and Numerical Methods #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical functions and polynomials #Meromorphic and Entire Functions #math.AP #math.CV #msc:35C10 #msc:35C20

paper · pdf · doi:10.48550/arxiv.1307.4627

29 pages

arxiv created 2013/07/17 · openalex publication_date 2013/07/17 · arxiv updated 2013/07/18 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We study a family of singularly perturbed q-difference-differential equations in the complex domain. We provide sectorial holomorphic solutions in the perturbation parameter ε. Moreover, we achieve the existence of a common formal power series in ε which represents each actual solution, and establish q-Gevrey estimates involved in this representation. The proof of the main result rests on a new version of the so-called Malgrange-Sibuya Theorem regarding q-Gevrey asymptotics. A particular Dirichlet like series is studied on the way.

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