On Parametric Gevrey Asymptotics for Singularly Perturbed Partial Differential Equations with Delays. (14th November 2013) - Lastra, Alberto; Malek, Stéphane
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.