Cauchy problems and applications
type: Item
instance of: scholarly article
title: Cauchy problems and applications
zbMATH Open document ID: 1025.34058
DOI: 10.12775/TMNA.2000.024
author: Chin-Yuan Lin
published in: Topological Methods in Nonlinear Analysis
publication date: 2003-06-01T00:00:00Z
review text: The author studies the Cauchy problem \[ {du\over dt}\in Au,\;t>0,\;u(0)=u_0, \] for \(u:[0,\infty)\to X\), where \(X\) is a real Banach space and \(A\) is a nonlinear multi-valued operator in \(X\) satisfying accretiveness and range conditions. Using the method of lines, the author shows that the problem has a limit solution. Under the hypothesis that \(A\) is `embeddedly demi-closed', it is shown that the limit solution is a strong solution. Further results are given for linear \(A\). The result is applied to nonlinear partial differential equations.
Mathematics Subject Classification ID: 34G25
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 47H20
zbMATH DE Number: 1545380
zbMATH Keywords: Cauchy problem
zbMATH Keywords: operator semigroup
zbMATH Keywords: accretive
reviewed by: Jürgen Voigt
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1545380