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...
| Autores: | , |
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| 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 |
| 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. |
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