On the Cauchy problem for quasilinear hyperbolic systems with a retarded argument
type: Item
instance of: scholarly article
title: On the Cauchy problem for quasilinear hyperbolic systems with a retarded argument
zbMATH Open document ID: 0637.35080
DOI: 10.1007/BF01769218
author: Jan Turo
author: Z. Kamont
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1986-01-01T00:00:00Z
review text: The author is concerned with quasilinear hyperbolic systems in the ``second canonic'' (or ``bicharacteristic'') form \[ (1)\quad \sum^{n}_{j=1}A_{ij}(x,y,z(x,y),(z\circ \alpha)(x,y))[\frac{\partial z_ j(x,y)}{dx}+ \] \[ +\sum^{m}_{k=1}\rho_{ik}(x,y,z(x,y),(z\circ \beta)(x,y))\frac{\partial z_ j(x,y)}{\partial y_ k}]= \] \[ =f_ i(x,y,z(x,y),(z\circ \gamma)(x,y)),\quad i=1,...,n, \] where \(z=(z_ 1,...,z_ n)\), \((z\circ \alpha)(x,y)=z(\alpha (x,y))\) and \(\alpha (x,y)=(\alpha_ 0(x,y),\alpha_ 1(x,y),...,\alpha_ m(x,y))\). For the problem obtained by adding to (1) the following initial condition \(z(0,x)=\phi (y)\), \(y\in R^ n\), a theorem on the existence and uniqueness of generalized solutions (in the sense ``almost everywhere'') is proved.
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 35L60
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 35A35
zbMATH DE Number: 4038379
zbMATH Keywords: retarded argument
zbMATH Keywords: iterative method
zbMATH Keywords: equation with time lag
zbMATH Keywords: quasilinear
zbMATH Keywords: bicharacteristic
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: generalized solutions
reviewed by: Z. Kamont
MaRDI profile type: Publication
cites work: Q3949408
cites work: Q4110014
cites work: Q4126782
cites work: Q3671567
cites work: Q4064426
cites work: Q4110015
cites work: Teoremi di esistenza per sistemi di equazioni quasi lineari a derivate parziali in piu variabili indipendenti
cites work: On the CAUCHY Problem for Non-linear Partial Differential-functional Equations of the First Order
cites work: On the Existence and Uniqueness of Solutions of the CAUCHY Problem for Linear Partial Differential – functional Equations of the First Order
cites work: Q4722488
full work available at URL: https://doi.org/10.1007/bf01769218
OpenAlex ID: W2092702639
description: scientific article; zbMATH DE number 4038379