Gevrey Versus q-Gevrey Asymptotic Expansions for Some Linear q-Difference-Differential Cauchy Problem
The asymptotic behavior of the analytic solutions of a family of singularly perturbed q-difference-differential equations in the complex domain is studied. Different asymptotic expansions with respect to the perturbation parameter and to the time variable are provided: one of Gevrey nature, and anot...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universidad de Alcalá (UAH) |
| Repositorio: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Idioma: | inglés |
| OAI Identifier: | oai:ebuah.uah.es:10017/64992 |
| Acceso en línea: | http://hdl.handle.net/10017/64992 https://dx.doi.org/https://doi.org/10.1007/s00025-024-02250-z |
| Access Level: | acceso abierto |
| Palabra clave: | Gevrey asymptotic expansions q-Gevrey asymptotic expansions Singularly perturbed Formal solution Matemáticas Mathematics |
| Sumario: | The asymptotic behavior of the analytic solutions of a family of singularly perturbed q-difference-differential equations in the complex domain is studied. Different asymptotic expansions with respect to the perturbation parameter and to the time variable are provided: one of Gevrey nature, and another of mixed type Gevrey and q-Gevrey. These asymptotic phenomena are observed due to the modification of the norm established on the space of coefficients of the formal solution. The techniques used are based on the adequate path deformation of the difference of two analytic solutions, and the application of several versions of Ramis-Sibuya theorem. |
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