On the summability of formal solutions for doubly singular nonlinear partial differential equations
type: Item
instance of: scholarly article
title: On the summability of formal solutions for doubly singular nonlinear partial differential equations
zbMATH Open document ID: 1250.35062
author: Stéphane Malek
published in: Journal of Dynamical and Control Systems
publication date: 2012-07-17T00:00:00Z
review text: The author studies singularly perturbed nonlinear PDEs of irregular type in the complex domain. Using the Borel-Laplace transforms he constructs actual holomorphic solutions of this problem. He shows that this holomorphic solutions have a common formal power series asymptotic expansion of Gevrey order 1 in the perturbation parameter.
Mathematics Subject Classification ID: 35C10
Mathematics Subject Classification ID: 35C20
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35R09
zbMATH DE Number: 6057757
zbMATH Keywords: Borel-Laplace transform
zbMATH Keywords: Cauchy problem
zbMATH Keywords: formal power series
zbMATH Keywords: nonlinear integro-differential equation
MaRDI profile type: Publication
full work available at URL: s10883-012-9134-7
OpenAlex ID: W1993405248
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DOI: 10.1007/S10883-012-9134-7
reviewed by: Igor Andrianov
description: scientific article; zbMATH DE number 6057757