Working Paper Article Version 1 This version is not peer-reviewed

On Gevrey Asymptotics for Linear Singularly Perturbed Equations with Linear Fractional Transforms

Version 1 : Received: 16 July 2020 / Approved: 17 July 2020 / Online: 17 July 2020 (15:42:50 CEST)

How to cite: Chen, G.; Lastra, A.; Malek, S. On Gevrey Asymptotics for Linear Singularly Perturbed Equations with Linear Fractional Transforms. Preprints 2020, 2020070396 Chen, G.; Lastra, A.; Malek, S. On Gevrey Asymptotics for Linear Singularly Perturbed Equations with Linear Fractional Transforms. Preprints 2020, 2020070396

Abstract

A family of linear singularly perturbed Cauchy problems is studied. The equations defining the problem combine partial differential operators together with the action of linear fractional transforms. The exotic geometry of the problem in the Borel plane, involving both sectorial regions and strip-like sets, gives rise to asymptotic results relating the analytic solution and the formal one through Gevrey asymptotic expansions. The main results lean on the appearance of domains in the complex plane which remain intimately related to Lambert W function, which turns out to be crucial in the construction of the analytic solutions.

Subject Areas

asymptotic expansion; Lambert W function; Borel-Laplace transform; Fourier transform; initial value problem; formal power series; singular perturbation

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