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On Boundary Layer Expansions for a Singularly Perturbed Problem with Confluent Fuchsian Singularities
Version 1
: Received: 23 December 2019 / Approved: 24 December 2019 / Online: 24 December 2019 (14:24:38 CET)
How to cite: Malek, S. On Boundary Layer Expansions for a Singularly Perturbed Problem with Confluent Fuchsian Singularities. Preprints 2019, 2019120323 Malek, S. On Boundary Layer Expansions for a Singularly Perturbed Problem with Confluent Fuchsian Singularities. Preprints 2019, 2019120323
Abstract
We consider a family of nonlinear singularly perturbed PDEs whose coefficients involve a logarithmic dependence in time with confluent Fuchsian singularities that unfold an irregular singularity at the origin and rely on a single perturbation parameter. We exhibit two distinguished finite sets of holomorphic solutions, so-called outer and inner solutions, by means of a Laplace transform with special kernel and Fourier integral. We analyze the asymptotic expansions of these solutions relatively to the perturbation parameter and show that they are (at most) of Gevrey order 1 for the first set of solutions and of some Gevrey order that hinges on the unfolding of the irregular singularity for the second.
Keywords
asymptotic expansion; Borel-Laplace transform; Fourier transform; initial value problem; formal power series; linear integro-differential equation; partial differential equation; singular perturbation
Subject
Computer Science and Mathematics, Analysis
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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