On Parametric Gevrey Asymptotics for Singularly Perturbed Partial Differential Equations with Delays | Zendy

Alberto Lastra | Zendy; Stéphane Malek | Zendy

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On Parametric Gevrey Asymptotics for Singularly Perturbed Partial Differential Equations with Delays

Author(s) -

Alberto Lastra,

Stéphane Malek

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/723040

Subject(s) - mathematics , holomorphic function , parametric statistics , perturbation (astronomy) , representation (politics) , domain (mathematical analysis) , series (stratigraphy) , singular perturbation , formal power series , mathematical analysis , power series , dirichlet distribution , law , boundary value problem , paleontology , statistics , physics , quantum mechanics , politics , political science , biology

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

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