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arXiv · 1508.02621

On parametric multilevel q-Gevrey asymptotics for some linear Cauchy problem

Alberto Lastra·Stéphane Malek
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Abstract

We study a linear $q-$difference-differential Cauchy problem, under the action of a perturbation parameter $ε$. This work deals with a $q-$analog of the research made in a previoues work, giving rise to a generalization of a recent work by the second author. 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.

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Alberto Lastra, Stéphane Malek. 2015-08-11. On parametric multilevel q-Gevrey asymptotics for some linear Cauchy problem. https://arxiv.org/abs/1508.02621

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