On multiscale Gevrey and q-Gevrey asymptotics for some linear q-difference differential initial value Cauchy problems
Analysis of PDEs
2016-07-08 v1 Complex Variables
Abstract
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.
Cite
@article{arxiv.1607.01986,
title = {On multiscale Gevrey and q-Gevrey asymptotics for some linear q-difference differential initial value Cauchy problems},
author = {Alberto Lastra and Stephane Malek},
journal= {arXiv preprint arXiv:1607.01986},
year = {2016}
}