Positive evolution families solving nonautonomous difference equations
type: Item
instance of: scholarly article
title: Positive evolution families solving nonautonomous difference equations
zbMATH Open document ID: 1273.47067
author: F. Bayazit
published in: Positivity
publication date: 2013-01-02T00:00:00Z
review text: The author considers the delay Cauchy problem \(\Phi(t,f_t)=0\) (\(t\geq s\in \mathbb{R}\)), \(f_s=g\in X\), where \(X\) is a space of \(\mathbb{C}^n\)-valued functions on \([0,1]\), \(f:[s,\infty)\to \mathbb{C}^n\), and \(\Phi(\cdot,\cdot):\mathbb{R}\times W^{1,1}([0,1],\mathbb{C}^n)\to \mathbb{C}^n\) takes the form \(\Phi(t,f)=f(1)-B(t)f(0)\) for matrices \(B(t)\in M_n(\mathbb{C})\) (\(t\in \mathbb{R}\)). By transferring the problem to a nonautonomous abstract Cauchy problem and using the corresponding evolution families, the author obtains some results on the wellposedness and asymptotic behavior of periodic evolution families for the delay Cauchy problem. Moreover, an application to flows in time-dependent networks is given.
reviewed by: Jin Liang
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 34G10
zbMATH DE Number: 6121301
zbMATH Keywords: evolution familiy
zbMATH Keywords: propagator
zbMATH Keywords: abstract Cauchy problem
zbMATH Keywords: Jacobs-Glicksberg-DeLeeuw decomposition
zbMATH Keywords: periodic process
zbMATH Keywords: flows in networks
MaRDI profile type: Publication
full work available at URL: s11117-011-0139-3
OpenAlex ID: W1985213327
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DOI: 10.1007/S11117-011-0139-3
description: scientific article; zbMATH DE number 6121301