On the multisummability of divergent solutions of linear partial differential equations with constant coefficients
type: Item
instance of: scholarly article
title: On the multisummability of divergent solutions of linear partial differential equations with constant coefficients
zbMATH Open document ID: 1195.35095
author: Sławomir Michalik
published in: Journal of Differential Equations
publication date: 2010-07-19T00:00:00Z
review text: The Cauchy problem for linear PDE in two complex variables with constant coefficients is studied. The author obtains necessary and sufficient conditions for the multisummability of formal solutions in terms of analytic continuation properties and growth estimates of the Cauchy data.
Mathematics Subject Classification ID: 35C10
Mathematics Subject Classification ID: 35E15
zbMATH DE Number: 5757638
zbMATH Keywords: linear PDE with constant coefficients
zbMATH Keywords: formal power series
zbMATH Keywords: Borel summability
zbMATH Keywords: multisummability
reviewed by: I. V. Andrianov
MaRDI profile type: Publication
full work available at URL: j.jde.2010.03.018
OpenAlex ID: W2059580070
cites work: Multisummability and Stokes multipliers of linear meromorphic differential equations
cites work: Multisummability of formal power series solutions of nonlinear meromorphic differential equations
cites work: On the Borel summability of divergent solutions of the heat equation
cites work: Divergent solutions of the heat equation: On an article of Lutz, Miyake and Schäfke
cites work: Summability of formal power-series solutions of partial differential equations with constant coefficients
cites work: Multisummability of formal power series solutions of partial differential equations with constant coefficients
cites work: Q4953935
cites work: Integral representation for Borel sum of divergent solution to a certain non-Kowalevski type equation
cites work: On the summability of formal solutions of linear partial differential equations
cites work: Summability of divergent solutions of the \(n\)-dimensional heat equation
cites work: Summability and fractional linear partial differential equations
cites work: Borel summability of divergent solutions of the Cauchy problem to non-Kowalewskian equations
cites work: Formal power series and linear systems of meromorphic ordinary differential equations
cites work: Q5699297
cites work: Q5582459
DOI: 10.1016/J.JDE.2010.03.018
Recommended article: Multisummability of formal solutions of inhomogeneous linear partial differential equations with constant coefficients
Recommended article: Corrigendum to: ``On the multisummability of divergent solutions of linear partial differential equations with constant coefficients''
Recommended article: Multisummability of formal solutions of some linear partial differential equations
Recommended article: Summability of formal solutions of linear partial differential equations with divergent initial data
Recommended article: Multisummability of formal solutions to the Cauchy problem for some linear partial differential equations
Recommended article: Multisummability of formal power series solutions of partial differential equations with constant coefficients
Recommended article: Multisummable solutions of nonlinear ordinary differential equations
Recommended article: On the summability of divergent power series solutions for certain first-order linear PDEs
Recommended article: On the summability of formal solutions of linear partial differential equations
Recommended article: On Multisummability of Formal Solutions with Logarithm Terms for Some Linear Partial Differential Equations
description: scientific article; zbMATH DE number 5757638