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July/August 2016 Multi-level Gevrey solutions of singularly perturbed linear partial differential equations
A. Lastra, S. Malek
Adv. Differential Equations 21(7/8): 767-800 (July/August 2016).

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.

Citation

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A. Lastra. S. Malek. "Multi-level Gevrey solutions of singularly perturbed linear partial differential equations." Adv. Differential Equations 21 (7/8) 767 - 800, July/August 2016.

Information

Published: July/August 2016
First available in Project Euclid: 3 May 2016

zbMATH: 1353.35033
MathSciNet: MR3493934

Subjects:
Primary: 35C10 , 35C20

Rights: Copyright © 2016 Khayyam Publishing, Inc.

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Vol.21 • No. 7/8 • July/August 2016
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