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...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2013 |
| Country: | España |
| Institution: | Universidad de Alcalá (UAH) |
| Repository: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Language: | English |
| OAI Identifier: | oai:ebuah.uah.es:10017/41435 |
| Online Access: | http://hdl.handle.net/10017/41435 https://dx.doi.org/10.1155/2013/723040 |
| Access Level: | Open access |
| Keyword: | q-difference-differential equations Singular perturbations Formal power series Borel-Laplace transform Borel summability q-Gevrey asymptotic expansions Matemáticas Mathematics |
| Summary: | 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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