Approximate controllability of second-order semilinear evolution systems with finite delay
type: Item
instance of: scholarly article
title: Approximate controllability of second-order semilinear evolution systems with finite delay
zbMATH Open document ID: 1480.34101
author: Xiaofeng Su
author: Xianlong Fu
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2021-08-17T00:00:00Z
review text: In the paper, the authors study second-order semilinear evolution equations with finite time delay. First, via proving the existence and uniqueness of mild solutions of the corresponding linear system the authors construct the fundamental solution and discuss regularity properties for it. After that, they present the mild solution of semilinear system via the fundamental solution of linear system using Laplace transform techniques. Then, the authors study the approximate controllability of the given system by employing the resolvent condition and obtain some sufficient conditions for approximate controllability. In the final part of the paper, the general results are illustrarated with an example.
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 34K35
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 7382611
zbMATH Keywords: approximate controllability
zbMATH Keywords: second-order evolution equation
zbMATH Keywords: fundamental solution
zbMATH Keywords: cosine operator
reviewed by: Vyacheslav I. Maksimov
MaRDI profile type: Publication
full work available at URL: s10255-021-1027-7
OpenAlex ID: W3187712763
cites work: Approximate controllability of second-order stochastic distributed implicit functional differential systems with infinite delay
cites work: Global existence and stability for second order functional evolution equations with infinite delay
cites work: On Concepts of Controllability for Deterministic and Stochastic Systems
cites work: Controllability of second-order differential inclusions in Banach spaces with nonlocal conditions
cites work: Controllability of second-order differential and integro-differential inclusions in Banach spaces
cites work: Q4848744
cites work: Ordinary differential equations in linear topological spaces. I
cites work: Q3678037
cites work: Approximate controllability of semilinear neutral retarded systems
cites work: Approximate controllability of semilinear neutral evolution systems with delay
cites work: Q3431856
cites work: Second order abstract neutral functional differential equations
cites work: Approximate controllability of second-order distributed implicit functional systems
cites work: Almost periodic solutions to abstract retarded functional differential equations with unbounded delay
cites work: Approximate controllability for semilinear retarded functional-differential equations
cites work: Approximate controllability for semilinear retarded systems
cites work: Asymptotically periodic solutions to some second-order evolution and difference equations
cites work: On cosine operator functions and one-parameter groups of operators
cites work: Asymptotic behavior for second order stochastic evolution equations with memory
cites work: Approximate controllability of second-order evolution differential inclusions in Hilbert spaces
cites work: Approximate controllability for a class of abstract second-order functional evolution equations
cites work: Approximate controllability of semi-linear neutral integro-differential systems with finite delay
cites work: Approximate controllability of a semi-linear neutral evolution system with infinite delay
cites work: Approximate controllability for semi-linear retarded stochastic systems in Hilbert spaces
cites work: Controllability of Semilinear Control Systems Dominated by the Linear Part
cites work: Stability results for second-order evolution equations with switching time-delay
cites work: Approximate controllability of stochastic differential systems driven by a Lévy process
cites work: Approximate Controllability of Second-Order Systems with State-Dependent Delay
cites work: Approximate controllability of fractional nonlinear differential inclusions
cites work: Approximate controllability of fractional stochastic differential inclusions with nonlocal conditions
cites work: APPROXIMATE CONTROLLABILITY OF SECOND-ORDER STOCHASTIC DIFFERENTIAL EQUATIONS WITH IMPULSIVE EFFECTS
cites work: Q4167185
cites work: Cosine families and abstract nonlinear second order differential equations
cites work: Q3903316
cites work: Approximate controllability for integrodifferential equations with multiple delays
cites work: On approximate controllability of second-order neutral partial stochastic functional integrodifferential inclusions with infinite delay and impulsive effects
DOI: 10.1007/S10255-021-1027-7
description: scientific article; zbMATH DE number 7382611