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2017 On Singular Solutions to PDEs with Turning Point Involving a Quadratic Nonlinearity
Stéphane Malek
Abstr. Appl. Anal. 2017: 1-32 (2017). DOI: 10.1155/2017/9405298


We study a singularly perturbed PDE with quadratic nonlinearity depending on a complex perturbation parameter ϵ. 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 C. We construct a family of sectorial meromorphic solutions obtained as a small perturbation in ϵ 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 ϵ 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.


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Stéphane Malek. "On Singular Solutions to PDEs with Turning Point Involving a Quadratic Nonlinearity." Abstr. Appl. Anal. 2017 1 - 32, 2017.


Received: 5 May 2017; Accepted: 1 August 2017; Published: 2017
First available in Project Euclid: 11 October 2017

zbMATH: 06929571
MathSciNet: MR3705453
Digital Object Identifier: 10.1155/2017/9405298

Rights: Copyright © 2017 Hindawi


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