Approximate controllability for semilinear retarded functional-differential equations
type: Item
instance of: scholarly article
title: Approximate controllability for semilinear retarded functional-differential equations
zbMATH Open document ID: 0962.93013
DOI: 10.1023/A:1021714500075
author: Yanyan Li
published in: Journal of Dynamical and Control Systems
publication date: 2000-04-13T00:00:00Z
review text: Semilinear, infinite-dimensional control systems with lumped and distributed delays are considered. It is generally assumed that the control system has both a linear part which contains the lumped and distributed delays and a nonlinear part without delays. Using the Leray-Schauder degree theory, a sufficient condition for approximate controllability in a given finite-time interval is formulated and proved. Moreover, the regularity of the solution of the abstract retarded differential equation is discussed. The relationships between the attainable sets for the semilinear control system and the corresponding linear control system are investigated. As an illustrative example, approximate controllability of the semilinear heat equation is considered. It should be pointed out that the results given in the paper extend the controllability considerations given in the paper [\textit{K. Naito}, J. Optimization Theory Appl. 60, 57-65 (1989; Zbl 0632.93007)].
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 34K35
Mathematics Subject Classification ID: 93C25
Mathematics Subject Classification ID: 93C23
zbMATH DE Number: 1431887
zbMATH Keywords: retarded functional equations
zbMATH Keywords: infinite-dimensional control systems
zbMATH Keywords: delays
zbMATH Keywords: Leray-Schauder degree theory
zbMATH Keywords: approximate controllability
zbMATH Keywords: semilinear control system
reviewed by: Jerzy Klamka
MaRDI profile type: Publication
full work available at URL: a:1021714500075
OpenAlex ID: W1976631336
description: scientific article; zbMATH DE number 1431887