Eindeutigkeitsaussagen für das Tricomi-Problem im \({\mathbb{R}}^ 2\) für eine Klasse nichtlinearer Gleichungen gemischten Typs
type: Item
instance of: scholarly article
title: Eindeutigkeitsaussagen für das Tricomi-Problem im \({\mathbb{R}}^ 2\) für eine Klasse nichtlinearer Gleichungen gemischten Typs
zbMATH Open document ID: 0532.35055
DOI: 10.1007/BF01380892
author: Manfred Schneider
published in: Monatshefte für Mathematik
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178163
review text: For the nonlinear equation \(L[u]:=k(y)u_{xx}+u_{yy}=g(x,y,u,u_ x,u_ y)\quad(sign k(y)=sign y)\) in G, bounded by a piecewise smooth curve \(\Gamma_ 0\) for \(y>0\) which intersects the line \(y=0\) at the points \(A(-1,0)\) and B(0,0) and for \(y<0\) by the characteristics \(\Gamma_ 1\) and \(\Gamma_ 2\) through the points A and B which intersect at the point C the uniqueness of boundary value problems \(i)\quad u|_{\Gamma_ 0\cup \Gamma_ 1}=\phi\) and \(ii)\quad d_ nu|_{\Gamma_ 0}=k(y)u_ xd_ y-u_ ydx=\phi ds\), \(u|_{\Gamma_ 1}=\psi\) is proved by the energy-integral method. To prove uniqueness theorems a growth condition for the function \(g_ u(...)\) in the hyperbolic part of the region is needed.
Mathematics Subject Classification ID: 35M99
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35G20
zbMATH DE Number: 3844249
zbMATH Keywords: Tricomi-problem
zbMATH Keywords: nonlinear equations of mixed type
zbMATH Keywords: uniqueness
zbMATH Keywords: energy- integral method
MaRDI profile type: Publication
cites work: On uniqueness of Frankl-Morawetz problem in \(\mathbb{R}^2\)
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description: scientific article; zbMATH DE number 3844249