On Parametric Gevrey Asymptotics for Singularly Perturbed Partial Differential Equations with Delays. (14th November 2013)

• Record Type: Journal Article
• Authors: Lastra, Alberto; Malek, Stéphane
• Other Names: Domoshnitsky Alexander Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-11-14
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/723040
• Languages: English
• ISSNs: 1085-3375

Abstract

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.