Multi-level Gevrey solutions of singularly perturbed linear partial differential equations
Complex Variables
2014-07-09 v1 Analysis of PDEs
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.
Cite
@article{arxiv.1407.2008,
title = {Multi-level Gevrey solutions of singularly perturbed linear partial differential equations},
author = {Alberto Lastra and Stéphane Malek},
journal= {arXiv preprint arXiv:1407.2008},
year = {2014}
}