Generalized Cauchy problem for hyperbolic functional differential systems
type: Item
instance of: scholarly article
title: Generalized Cauchy problem for hyperbolic functional differential systems
zbMATH Open document ID: 1215.35162
DOI: 10.1216/RMJ-2011-41-1-205
author: Z. Kamont
published in: Rocky Mountain Journal of Mathematics
publication date: 2011-03-01T00:00:00Z
review text: It is considered the following system \[ \partial_tz_i(t,x)=f_i(t,x,z_{\psi(t,x)},\partial_xz_i(t,x)), \quad i=1,\dots,k, \] with the initial condition \[ z_i(t,x)=\varphi_i(t,x) \quad\text{on}\quad E_{0.i}, \] where \(E_{0.i}=[-d_0,a_i]\times\mathbb R^n\). The existence of a weak solution of the system is proved by using a method of successive approximation. The theory of bicharacteristics and integral inequalities is applied. The existence results can be applied to differential systems with deviated arguments and differential integral problems.
reviewed by: Leonid Berezansky
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 35R45
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5858886
zbMATH Keywords: functional differential systems
zbMATH Keywords: generalized Cauchy problem
zbMATH Keywords: bicharacteristics
zbMATH Keywords: weak solutions
MaRDI profile type: Publication
cites work: Q5531903
cites work: Existence, uniqueness and continuous dependence for a hereditary nonlinear functional partial differential equation of the first order
cites work: Existence of generalized solutions of hyperbolic functional-differential equations
cites work: Generalized solutions to boundary value problems for quasilinear hyperbolic systems of partial differential-functional equations
cites work: Q4005690
cites work: Q4196866
cites work: Q3485364
cites work: On the local Cauchy problem for Hamilton Jacobi equations with a functional dependence
cites work: Q4699469
cites work: Q3134809
cites work: Q3909393
cites work: Nonlinear hyperbolic volterra integrodifferential equations
cites work: Q4122271
cites work: Mixed problems for quasilinear hyperbolic systems
cites work: Q5769119
description: scientific article; zbMATH DE number 5858886