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...

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Detalles Bibliográficos
Autores: Dreyfus, Thomas, Lastra Sedano, Alberto|||0000-0002-4012-6471, Malek, Stephane
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
Descripción
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.