%0 Journal Article 
%A Lastra Sedano, Alberto
%A Malek, Stephane
%T On multiscale Gevrey and q-Gevrey asymptotics for some linear q-difference-differential initial value Cauchy problems
%D 2017
%@ 1023-6198
%U http://hdl.handle.net/10017/41440
%X 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.
%K Asymptotic expansion
%K Borel-Laplace transform
%K Fourier transform
%K Cauchy problem
%K Formal power series
%K Nonlinear integro-differential equation
%K Nonlinear partial differential equation
%K Singular perturbation
%K Matemáticas
%K Mathematics
%~ Biblioteca Universidad de Alcala