On multiscale Gevrey and q-Gevrey asymptotics for some linear q-difference-differential initial value Cauchy problems

We study the asymptotic behavior of the solutions related to a singularly perturbed q-difference-differential problem in the complex domain. The analytic solution can be splitted according to the nature of the equation and its geometry so that both, Gevrey and q-Gevrey asymptotic phenomena are obser...

Descripción completa

Detalles Bibliográficos
Autores: Lastra Sedano, Alberto|||0000-0002-4012-6471, Malek, Stephane
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/41440
Acceso en línea:http://hdl.handle.net/10017/41440
https://dx.doi.org/10.1080/10236198.2017.1337104
Access Level:acceso abierto
Palabra clave:Asymptotic expansion
Borel-Laplace transform
Fourier transform
Cauchy problem
Formal power series
Nonlinear integro-differential equation
Nonlinear partial differential equation
Singular perturbation
Matemáticas
Mathematics
Descripción
Sumario:We study the asymptotic behavior of the solutions related to a singularly perturbed q-difference-differential problem in the complex domain. The analytic solution can be splitted according to the nature of the equation and its geometry so that both, Gevrey and q-Gevrey asymptotic phenomena are observed and can be distinguished, relating the analytic and the formal solution. The proof leans on a two level novel version of Ramis-Sibuya theorem under Gevrey and q-Gevrey orders.