On the summability of formal solutions of nonlinear partial differential equations with shrinkings
type: Item
instance of: scholarly article
title: On the summability of formal solutions of nonlinear partial differential equations with shrinkings
zbMATH Open document ID: 1116.35037
author: Stéphane Malek
published in: Journal of Dynamical and Control Systems
publication date: 2007-06-07T00:00:00Z
review text: Nonlinear PDEs with deviating variables are under consideration. The author gives sufficient conditions for the existence and uniqueness of formal series in the variable \(t\). He also obtains new sufficient conditions, both on the shape of governing equation and on initial conditions, under which constructed formal series solutions are 1-summable.
Mathematics Subject Classification ID: 35C10
Mathematics Subject Classification ID: 35C20
zbMATH DE Number: 5162415
zbMATH Keywords: nonlinear PDE
zbMATH Keywords: Cauchy problem
zbMATH Keywords: shrinking
zbMATH Keywords: asymptotic estimation
zbMATH Keywords: power series solution
zbMATH Keywords: Borel summability
zbMATH Keywords: Gevrey estimate
reviewed by: I. V. Andrianov
MaRDI profile type: Publication
full work available at URL: s10883-006-9007-z
OpenAlex ID: W2076737706
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DOI: 10.1007/S10883-006-9007-Z
description: scientific article; zbMATH DE number 5162415