Working Paper Article Version 1 This version is not peer-reviewed

Parametric Gevrey Asymptotics in Two Complex Time Variables through Truncated Laplace Transforms

Version 1 : Received: 2 April 2020 / Approved: 3 April 2020 / Online: 3 April 2020 (15:35:10 CEST)
Version 2 : Received: 12 June 2020 / Approved: 14 June 2020 / Online: 14 June 2020 (13:06:30 CEST)

How to cite: Malek, S.; Lastra, A.; Chen, G. Parametric Gevrey Asymptotics in Two Complex Time Variables through Truncated Laplace Transforms. Preprints 2020, 2020040038 Malek, S.; Lastra, A.; Chen, G. Parametric Gevrey Asymptotics in Two Complex Time Variables through Truncated Laplace Transforms. Preprints 2020, 2020040038

Abstract

The work is devoted to the study of a family of linear initial value problems of partial differential equations in the complex domain, dealing with two complex time variables. The use of a truncated Laplace-like transformation in the construction of the analytic solution allows to overcome a small divisor phenomenon arising from the geometry of the problem and represents an alternative approach to the one proposed in a recent work by the last two authors. The result leans on the application of a fixed point argument and the classical Ramis-Sibuya theorem.

Subject Areas

asymptotic expansion; Borel-Laplace transform; Fourier transform; initial value problem; formal power series; partial differential equation; singular perturbation

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