Functional characteristic initial value problems
type: Item
instance of: scholarly article
title: Functional characteristic initial value problems
zbMATH Open document ID: 0585.35067
DOI: 10.1016/0022-247X(85)90322-1
author: B. George
published in: Journal of Mathematical Analysis and Applications
publication date: 1985-01-01T00:00:00Z
review text: The authors study the hyperbolic equations with delays \(\sigma\) and \(\tau\) of the form \[ u_{xy}\pm f(x,y,u(x-\sigma,y-\tau))=0, \] with characteristic initial data \(u(x,y)=\phi (x,y)\) if \(-\sigma \leq x<\infty\), -\(\tau\leq y\leq 0\) and \(u(x,y)=\psi (x,y)\) if -\(\sigma\leq x\leq 0\), and \(-\tau \leq y<\infty\). Here f, \(\phi\), \(\psi\), are continuous, f is positive and \(f(x,y,0)=0\). The paper contains a study of the effects of the delays on the oscillatory nature of the solutions.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35R10
zbMATH DE Number: 3937682
zbMATH Keywords: hyperbolic equations
zbMATH Keywords: delays
zbMATH Keywords: oscillatory nature of the solutions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3937682