On \(x\)-analytic solutions to the Cauchy problem for partial differential equations with retarded variables
type: Item
instance of: scholarly article
title: On \(x\)-analytic solutions to the Cauchy problem for partial differential equations with retarded variables
zbMATH Open document ID: 0847.35029
DOI: 10.4171/ZAA/704
author: Antoni Augustynowicz
author: Henryk Leszczyński
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1996-10-20T00:00:00Z
review text: Summary: We prove some existence results for solutions analytic with respect to the spatial variables to the Cauchy problem for the first-order equation \[ D_t u(t, x)= g(t, x, u(\alpha(t), \beta(t, x)), D_x u(\gamma(t), \delta(t, x))) \] with a dealy and some deviations not only at the function, but also at its derivative. We construct a natural Banach space and a norm which make an adequate integral operator contractive. Due to a useful relation of partial order in this space the main problem is also placed in the theory of monotone iterative techniques.
Mathematics Subject Classification ID: 35F25
Mathematics Subject Classification ID: 35R10
zbMATH DE Number: 889001
zbMATH Keywords: Banach contraction principle
zbMATH Keywords: Bielecki's norm
zbMATH Keywords: monotone iterative techniques
MaRDI profile type: Publication
cites work: Q3231397
cites work: Partial differential equations. 2nd ed
cites work: Q3807603
cites work: Functional differential equations of the Cauchy-Kowalevsky type
full work available at URL: https://doi.org/10.4171/zaa/704
OpenAlex ID: W1989623665
description: scientific article; zbMATH DE number 889001