On the Cauchy-Kowalewski theorem for characteristic initial surfaces
type: Item
instance of: scholarly article
title: On the Cauchy-Kowalewski theorem for characteristic initial surfaces
zbMATH Open document ID: 0627.35002
author: Katasuju Igari
published in: Proceedings of the Japan Academy. Series A
publication date: 1987-01-01T00:00:00Z
review text: Im \({\mathbb{C}}^{n+1}\) (t\(\in {\mathbb{C}}\), \(x\in {\mathbb{C}}^ n)\) sei \[ P(t,x;\partial_ t,\partial_ x)=\sum^{m}_{s=0}\sum_{| \alpha | \leq s}a_{m-s,\alpha}(t,x)\partial_ t^{m-s} \partial_ x^{\alpha}. \] Für den Fall, daß die Anfangsfläche \(t=0\) charakteristisch, aber nicht einfach charakteristisch ist, wird das Cauchy Problem (P,m-1) in der Klasse der holomorphen Funktionen untersucht (Vorgabe von \(\partial^ k_ tu|_{t=0}\) für \(k=0,1,...,m-2).\) Es werden hinreichende Koeffizienten-Bedingungen angegeben (die z.B. für Gleichungen vom Fuchs-Typ erfüllt sind) für die eindeutige Lösbarkeit des Cauchy-Problems. Der Beweis wird angedeutet.
Mathematics Subject Classification ID: 35A10
Mathematics Subject Classification ID: 35G05
zbMATH DE Number: 4019548
zbMATH Keywords: holomorphic functions
zbMATH Keywords: non-characteristic
zbMATH Keywords: Fuchs type operator
zbMATH Keywords: variable multiplicity
zbMATH Keywords: characteristics
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: Cauchy Problem
reviewed by: Joachim Jaenicke
MaRDI profile type: Publication
full work available at URL: pjaa.63.7
OpenAlex ID: W2005384470
cites work: Cauchy problems with characteristic initial hypersurface
cites work: On the initial-value problems with data on a double characteristic
cites work: Les equations aux derivees partielles ayant des surfaces caracteristiques dutype de fuchs
cites work: Solutions nulles et solutions non analytiques
cites work: On the theorem of Cauchy-Kowalevsky for first order linear differential equations with degenerate principal symbols
DOI: 10.3792/PJAA.63.7
description: scientific article; zbMATH DE number 4019548