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<p>A novel asymptotic representation of the analytic solutions to a family of singularly perturbed <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13324_2025_1074_Article_IEq2.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\(q-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>difference-differential equations in the complex domain is obtained. Such asymptotic relation shows two different levels associated to the vanishing rate of the domains of the coefficients in the formal asymptotic expansion. On the way, a novel version of a multilevel sequential Ramis-Sibuya type theorem is achieved.</p>

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On parametric \(0-\)Gevrey asymptotic expansions in two levels for some linear partial \(q-\)difference-differential equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月15日

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  • Alberto Lastra,
  • Stéphane Malek

摘要

A novel asymptotic representation of the analytic solutions to a family of singularly perturbed \(q-\) q - difference-differential equations in the complex domain is obtained. Such asymptotic relation shows two different levels associated to the vanishing rate of the domains of the coefficients in the formal asymptotic expansion. On the way, a novel version of a multilevel sequential Ramis-Sibuya type theorem is achieved.