Alberto LASTRA, Stephane MALEK
On parametric multilevel q-Gevrey asymptotics for some linear q-difference-differential equations
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ABSTRACT. We study linear q-difference-differential equations, under the action of a perturbation parameter. This work deals with a q-analog of the research made recently by the two authors on singularly perturbed nonlinear initial value problems. This generalization is related to the nature of the forcing term which suggests the use of a q-analog of an acceleration procedure. The proof leans on a q-analog of the so-called Ramis-Sibuya theorem which entails two distinct q-Gevrey orders. The work concludes with an application of the main result when the forcing term solves a related problem.