On singular solutions to PDEs with turning point involving a quadratic nonlinearity
type: Item
instance of: scholarly article
title: On singular solutions to PDEs with turning point involving a quadratic nonlinearity
zbMATH Open document ID: 1470.35140
DOI: 10.1155/2017/9405298
author: Stéphane Malek
published in: Abstract and Applied Analysis
publication date: 2018-08-30T00:00:00Z
review text: Summary: We study a singularly perturbed PDE with quadratic nonlinearity depending on a complex perturbation parameter \(\varepsilon\). The problem involves an irregular singularity in time, as in a recent work of the author and A. Lastra, but possesses also, as a new feature, a turning point at the origin in \(\mathbb{C}\). We construct a family of sectorial meromorphic solutions obtained as a small perturbation in \(\varepsilon\) of a slow curve of the equation in some time scale. We show that the nonsingular parts of these solutions share common formal power series (that generally diverge) in \(\varepsilon\) as Gevrey asymptotic expansion of some order depending on data arising both from the turning point and from the irregular singular point of the main problem.
Mathematics Subject Classification ID: 35G20
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35C20
zbMATH DE Number: 6929571
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/9405298
OpenAlex ID: W2755120973
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description: scientific article; zbMATH DE number 6929571