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

2016/07/07 by Alberto Lastra, Lastra, Alberto, Stephane Malek +1
Mathematics · #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #math.AP #math.CV

paper · pdf · doi:10.48550/arxiv.1607.01986

arxiv created 2016/07/07 · arxiv updated 2016/07/08

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.

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