Some notes on parametric multilevel q-Gevrey asymptotics for some linear q-difference-differential equations (Algebraic analytic methods in complex partial differential equations)

This manuscript pretends to provide a survey of the work [8], which has been presented in RIMS Symposium Algebraic Analytic Methods in Complex Partial Differential Equations. The concise scheme in these notes aims to give a clear idea on the procedure followed in that work, as well as to clarify the steps underlying in the results in [8]. In the work [8], we study a family of linear q-difference-differential equations, under the action of a perturbation parameter $epsilon$ . The procedure leans on a q-analog of an acceleration procedure and a q-analog of Ramis-Sibuya theorem in two levels, based on the ideas of the one-level result in [2]