Advances in Differential Equations

Multi-level Gevrey solutions of singularly perturbed linear partial differential equations

A. Lastra and S. Malek

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Abstract

We study the asymptotic behavior of the solutions related to a family of singularly perturbed linear partial differential equations in the complex domain. The analytic solutions obtained by means of a Borel-Laplace summation procedure are represented by a formal power series in the perturbation parameter. Indeed, the geometry of the problem gives rise to a decomposition of the formal and analytic solutions so that a multi-level Gevrey order phenomenon appears. This result leans on a Malgrange-Sibuya theorem in several Gevrey levels.

Article information

Source
Adv. Differential Equations Volume 21, Number 7/8 (2016), 767-800.

Dates
First available in Project Euclid: 3 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.ade/1462298657

Mathematical Reviews number (MathSciNet)
MR3493934

Zentralblatt MATH identifier
1353.35033

Subjects
Primary: 35C10: Series solutions 35C20: Asymptotic expansions

Citation

Lastra, A.; Malek, S. Multi-level Gevrey solutions of singularly perturbed linear partial differential equations. Adv. Differential Equations 21 (2016), no. 7/8, 767--800. https://projecteuclid.org/euclid.ade/1462298657.


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