On Parametric Gevrey Asymptotics for Singularly Perturbed Partial Differential Equations with Delays
Open Access
- 14 November 2013
- journal article
- research article
- Published by Hindawi Limited in Abstract and Applied Analysis
- Vol. 2013, 1-18
- https://doi.org/10.1155/2013/723040
Abstract
We study a family of singularly perturbed -difference-differential equations in the complex domain. We provide sectorial holomorphic solutions in the perturbation parameter . Moreover, we achieve the existence of a common formal power series in which represents each actual solution and establish -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 -Gevrey asymptotics. A particular Dirichlet like series is studied on the way.Keywords
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