关于某些线性偏 $q$-差分-微分方程的参数 $0$-Gevrey 两级渐近展开

arXiv - MATH - Complex Variables Pub Date : 2024-08-22 DOI:arxiv-2408.12335

Alberto Lastra, Stephane Malek

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引用次数: 0

摘要

研究获得了复域中一系列奇异扰动 $q-$ 差分微分方程解析解的一种新的渐近表示。这种渐近关系显示了与形渐近展开中系数域的消失率相关的两个不同层次。在此过程中，实现了多级序列 Ramis-Sibuya 型定理的新版本。

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

A novel asymptotic representation of the analytic solutions to a family of singularly perturbed $q-$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.

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arXiv - MATH - Complex Variables

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