3 Citations (Scopus)

Abstract

In this paper we prove, under suitable hypotheses, eventually norm continuity and compactness of the solution semigroups of certain neutral differential equations in Banach spaces. Our approach is based on a general perturbation theorem obtained from closed-loop systems of infinite dimensional control systems with unbounded control and observation operators. In fact, the solution semigroup can be viewed as the semigroup of an appropriate closed-loop system in product state spaces.

Original languageEnglish
Pages (from-to)543-552
Number of pages10
JournalJournal of Mathematical Analysis and Applications
Volume375
Issue number2
DOIs
Publication statusPublished - 15 Mar 2011

Fingerprint

Banach spaces
Closed loop systems
Semigroup
Banach space
Norm
Closed-loop System
Neutral Differential Equation
Infinite-dimensional Systems
Differential equations
Product Space
Control systems
Compactness
State Space
Control System
Perturbation
Operator
Theorem

Keywords

  • Banach space
  • Compactness
  • Neutral semigroup
  • Norm continuity
  • Perturbation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Eventual norm continuity for neutral semigroups on Banach spaces. / Hadd, S.; Nounou, Hazem; Nounou, Mohamed.

In: Journal of Mathematical Analysis and Applications, Vol. 375, No. 2, 15.03.2011, p. 543-552.

Research output: Contribution to journalArticle

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AB - In this paper we prove, under suitable hypotheses, eventually norm continuity and compactness of the solution semigroups of certain neutral differential equations in Banach spaces. Our approach is based on a general perturbation theorem obtained from closed-loop systems of infinite dimensional control systems with unbounded control and observation operators. In fact, the solution semigroup can be viewed as the semigroup of an appropriate closed-loop system in product state spaces.

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