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arXiv · 1307.4627

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

Alberto Lastra·Stéphane Malek
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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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Alberto Lastra, Stéphane Malek. 2013-07-17. On parametric Gevrey asymptotics for singularly perturbed partial differential equations with delays. https://arxiv.org/abs/1307.4627

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