13-62 A. Lastra, S. Malek

On parametric Gevrey asymptotics for singularly perturbed partial differential equations with delays (570K, pdf) Jul 17, 13

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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. Moreover, we achieve the existence of a common formal power series in this parameter 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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