Qualitative behaviour of solutions of the Goursat problem for hyperbolic differential equations
type: Item
instance of: scholarly article
title: Qualitative behaviour of solutions of the Goursat problem for hyperbolic differential equations
zbMATH Open document ID: 0653.35050
DOI: 10.1016/0898-1221(87)90171-4
author: S. H. Smith
publication date: 1987-01-01T00:00:00Z
review text: This work is an extension of the studies on solutions of the Goursat problem in the quarter space to the case in the domain: \(D=\{(x,y):\quad x\geq 0,0\leq y\leq g(x)\},\) where g is strictly increasing. Specifically the problem treated here is to establish oscillation criteria and to determine the asymptotic behavior of solutions of the problem \[ u_{xy}+p(x,y)u=0,\quad x>0,\quad 0<y<g(x),\quad u(x,0)=\phi (x),\quad x>0,\quad u(x,g(x))=\psi (x),\quad x>0. \] The author shows the existence of non-oscillatory solution as well as an oscillatory criteria.
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 4065528
zbMATH Keywords: Goursat problem
zbMATH Keywords: oscillation criteria
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: existence
zbMATH Keywords: non-oscillatory solution
reviewed by: Akira Tsutsumi
MaRDI profile type: Publication
full work available at URL: 0898-1221(87)90171-4
OpenAlex ID: W2032652166
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4065528