Hyperbolic functional-differential equations with unbounded delay
type: Item
instance of: scholarly article
title: Hyperbolic functional-differential equations with unbounded delay
zbMATH Open document ID: 0924.35187
DOI: 10.4171/ZAA/871
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1999-11-11T00:00:00Z
full work available at URL: https://eudml.org/doc/48274
review text: The author studies the existence and uniqueness of Carathéodory solutions for quasilinear equations with unbounded delay \[ D_t z(t,x) +\sum^n_{i=1} \rho_i (t,x,z_{(t,x)}) D_{x_i} z(t,x)= f(t,x,z_{(t,x)}), \] \[ z(t,x)= \varphi(t,x) \quad\text{on} \quad (-\infty,0] \times \mathbb{R}^n, \] where \(z_{(t,x)} (\tau,s)= z(t+ \tau,x+s)\), \((\tau,s)\in D\). To this end, the method of bicharacteristics and the method of integral inequalities are used.
reviewed by: Drumi Bainov
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 1278888
zbMATH Keywords: unbounded delay
zbMATH Keywords: local existence
zbMATH Keywords: Carathéodory solutions
author: Z. Kamont
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1278888