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

2014/07/08 by Alberto Lastra, Lastra, Alberto, Stéphane Malek +1 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1407.2008

openalex publication_date 2014/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic behavior of the solutions related to a family of\nsingularly perturbed linear partial differential equations in the complex\ndomain. The analytic solutions obtained by means of a Borel-Laplace summation\nprocedure are represented by a formal power series in the perturbation\nparameter. Indeed, the geometry of the problem gives rise to a decomposition of\nthe formal and analytic solutions so that a multi-level Gevrey order phenomenon\nappears. This result leans on a Malgrange-Sibuya theorem in several Gevrey\nlevels.\n

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