On the multiple-scale analysis for some linear partial q-difference and differential equations with holomorphic coeffcients
We consider analytic and formal solutions of certain family of q-difference-differential equations under the action of a complex perturbation parameter. The previous study (Lastra and Malek in Adv. Differ. Equ. 2015:344, 2015) provides information in the case where the main equation under study is f...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad de Alcalá (UAH) |
| Repositorio: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Idioma: | inglés |
| OAI Identifier: | oai:ebuah.uah.es:10017/41534 |
| Acceso en línea: | http://hdl.handle.net/10017/41534 https://dx.doi.org/10.1186/s13662-019-2263-5 |
| Access Level: | acceso abierto |
| Palabra clave: | Asymptotic expansion Borel-Laplace transform Fourier transform Formal power series Singular perturbation q-difference-differential equation Matemáticas Mathematics |
| Sumario: | We consider analytic and formal solutions of certain family of q-difference-differential equations under the action of a complex perturbation parameter. The previous study (Lastra and Malek in Adv. Differ. Equ. 2015:344, 2015) provides information in the case where the main equation under study is factorizable as a product of two equations in the so-called normal form. Each of them gives rise to a single level of q-Gevrey asymptotic expansion. In the present work, the main problem under study does not suffer any factorization, and a different approach is followed. More precisely, we lean on the technique developed in (Dreyfus in Int. Math. Res. Not. 15:6562-6587, 2015, where the first author makes distinction among the different q-Gevrey asymptotic levels by successive applications of two q-Borel-Laplace transforms of different orders, both to the same initial problem, which can be described by means of a Newton polygon. |
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