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

Stephane Malek; Alberto Lastra; Guoting Chen

Working Paper Article Version 2 This version is not peer-reviewed

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)

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 first two authors. The result leans on the application of a fixed point argument and the classical Ramis-Sibuya theorem.

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

Computer Science and Mathematics, Analysis

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

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