On a class of systems of nonlinear partial differential equations in several independent variables
type: Item
instance of: scholarly article
title: On a class of systems of nonlinear partial differential equations in several independent variables
zbMATH Open document ID: 0575.35007
DOI: 10.1007/BF01776851
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1985-01-01T00:00:00Z
review text: Betrachtet wird das nichtlineare Gleichungssystem \[ (a)\quad p^{(i)}(x,y_ 1,...,y_ r)+ \] \[ f_ i(x,y_ 1,...,y_ r,z^{(1)}(x,y_ 1,...,y_ r),...,z^{(m)},q_ 1^{(1)},...,q_ r^{(m)})=0, \] wobei \(p^{(i)}(x,y_ 1,...,y_ r):=\partial z^{(i)}(x,y_ 1,...,y_ r)/\partial x,\quad q_ k^{(i)}(x,y_ 1,...,y_ r)=\partial z^{(i)}(x,y_ 1,...,y_ r)/\partial y_ k\quad (1\leq i\leq m,\quad 1\leq k\leq r).\) Außerdem werden die r Gleichungssysteme betrachtet, die man durch Differentiation von (a) nach \(y_{\ell}\), \(1\leq \ell \leq r\), erhält. Es werden Bedingungen formuliert, unter denen jedes der letztgenannten Systeme in bicharakteristische Form überführt werden kann. Unter diesen Voraussetzungen werden für (a) Sätze über die Existenz der Lösung des Cauchyproblems sowie über die stetige Abhängigkeit von Anfangswerten bewiesen.
Mathematics Subject Classification ID: 35F25
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35B30
zbMATH DE Number: 3918883
zbMATH Keywords: Cauchy problem
zbMATH Keywords: existence
zbMATH Keywords: bicharacteristic form
zbMATH Keywords: continuous dependence
author: Maria Cinquini-Cibrario
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3918883