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

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 -Ge...

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Detalles Bibliográficos
Autores: Lastra Sedano, Alberto|||0000-0002-4012-6471, Malek, Stephane
Tipo de recurso: artículo
Fecha de publicación:2013
País:España
Institución:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/41435
Acceso en línea:http://hdl.handle.net/10017/41435
https://dx.doi.org/10.1155/2013/723040
Access Level:acceso abierto
Palabra clave:q-difference-differential equations
Singular perturbations
Formal power series
Borel-Laplace transform
Borel summability
q-Gevrey asymptotic expansions
Matemáticas
Mathematics
Descripción
Sumario: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.