Strongly Regular Multi-level Solutions of Singularly Perturbed Linear Partial Differential Equations

被引：9

作者：

Lastra, A. ^{[1
]}

Malek, S. ^{[2
]}

Sanz, J. ^{[3
]}

机构：

[1] Univ Alcala, Dept Fis & Matemat, Ap Correos 20, Madrid 28871, Spain

[2] Univ Lille 1, Lab Paul Painleve, F-59655 Villeneuve Dascq, France

[3] Univ Valladolid, IMUVA, Dept Algebra Anal Matemat Geometria & Topol, Paseo Belen 7,Campus Miguel Delibes, E-47011 Valladolid, Spain

来源：

RESULTS IN MATHEMATICS | 2016年 / 70卷 / 3-4期

关键词：

Linear partial differential equations; singular perturbations; formal power series; Borel-Laplace transform; Borel summability; Gevrey asymptotic expansions; strongly regular sequence; FUCHSIAN HYPERBOLIC-EQUATIONS; POWER-SERIES SOLUTIONS; FORMAL SOLUTIONS; SUMMABILITY; SMOOTHNESS; SPACES;

D O I：

10.1007/s00025-015-0493-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the asymptotic behavior of the solutions related to a family of singularly perturbed partial differential equations in the complex domain. The analytic solutions are asymptotically represented by a formal power series in the perturbation parameter. The geometry of the problem and the nature of the elements involved in it give rise to different asymptotic levels related to the so-called strongly regular sequences. The result leans on a novel version of a multi-level Ramis-Sibuya theorem.

引用

页码：581 / 614

页数：34

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