Initial boundary value problems for the Carleman equation
type: Item
instance of: scholarly article
title: Initial boundary value problems for the Carleman equation
zbMATH Open document ID: 0544.35065
DOI: 10.1016/0898-1221(83)90065-2
publication date: 1983-01-01T00:00:00Z
review text: The author utilizes the theory of nonlinear evolution operators to investigate the coupled first order hyperbolic system \[ \partial u/\partial t+\partial u/\partial x+u^ 2-v^ 2=0\quad u(0,t)=g(t),\quad v(1,t)=h(t) \] \[ \partial v/\partial t-\partial v/\partial x+v^ 2-u^ 2=0\quad u(x,0)=u_ 0(x),\quad v(x,0)=v_ 0(x) \] He associates a nonlinear evolution system in \(L^ 1(0,1)\) with (1); this system is generated by a family of nonlinear accretive operators of varying domain. In case that the boundary conditions are constant, the system is autonomous. Consequently the evolution operator is a nonlinear semigroup.
Mathematics Subject Classification ID: 35L60
Mathematics Subject Classification ID: 47H06
Mathematics Subject Classification ID: 47H20
zbMATH DE Number: 3865839
zbMATH Keywords: Carleman equation
zbMATH Keywords: nonlinear evolution operators
zbMATH Keywords: nonlinear accretive operators
zbMATH Keywords: varying domain
author: W. E. Fitzgibbon
reviewed by: Gerard Hecquet
MaRDI profile type: Publication
full work available at URL: 0898-1221(83)90065-2
OpenAlex ID: W2068127119
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 3865839