Boundary layer expansions for initial value problems with two complex time variables

Boundary layer expansions for initial value problems with two complex time variables

Abstract We study a family of partial differential equations in the complex domain, under the action of a complex perturbation parameter ϵ. We construct inner and outer solutions of the problem and relate them to asymptotic representations via Gevrey asymptotic expansions with respect to ϵ in adequa...

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Bibliographic Details
Main Authors: A. Lastra, S. Malek
Format: Article
Language:English
Published: SpringerOpen 2020-01-01
Series:Advances in Difference Equations
Subjects:
Asymptotic expansion
Borel–Laplace transform
Fourier transform
Initial value problem
Formal power series
Boundary layer
Online Access:https://doi.org/10.1186/s13662-020-2496-3
Description
Summary:Abstract We study a family of partial differential equations in the complex domain, under the action of a complex perturbation parameter ϵ. We construct inner and outer solutions of the problem and relate them to asymptotic representations via Gevrey asymptotic expansions with respect to ϵ in adequate domains. The asymptotic representation leans on the cohomological approach determined by the Ramis–Sibuya theorem.
ISSN:1687-1847

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