Control problems for semilinear neutral differential equations in Hilbert spaces.

Jin-Mun Jeong,Seong Ho Cho

doi:10.1155/2014/431978

Jin-Mun Jeong, Seong Ho Cho

Open Access

https://doi.org/10.1155/2014/431978

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Journal: TheScientificWorldJournal	Publication Date: Jan 1, 2014
Citations: 20	License type: CC BY 3.0

Affiliation: Pukyong National University

Abstract

We construct some results on the regularity of solutions and the approximate controllability for neutral functional differential equations with unbounded principal operators in Hilbert spaces. In order to establish the controllability of the neutral equations, we first consider the existence and regularity of solutions of the neutral control system by using fractional power of operators and the local Lipschitz continuity of nonlinear term. Our purpose is to obtain the existence of solutions and the approximate controllability for neutral functional differential control systems without using many of the strong restrictions considered in the previous literature. Finally we give a simple example to which our main result can be applied.

Highlights

Let H and V be real Hilbert spaces such that V is a dense subspace in H
We are concerned with the global existence of solution and the approximate controllability for the following abstract neutral functional differential system in a Hilbert space H: d dt
We propose a different approach from the earlier works

Summary

Introduction

Let H and V be real Hilbert spaces such that V is a dense subspace in H. We are concerned with the global existence of solution and the approximate controllability for the following abstract neutral functional differential system in a Hilbert space H:. The second purpose of this paper is to study the approximate controllability for the neutral equation (1) based on the regularity for (1); namely, the reachable set of trajectories is a dense subset of H. This kind of equations arises naturally in biology, physics, control engineering problem, and so forth. Our purpose in this paper is to obtain the existence of solutions and the approximate controllability for neutral functional differential control systems without using many of the strong restrictions considered in the previous literature. We give a simple example to which our main result can be applied

Notations

Regularity for Linear Equations

Semilinear Differential Equations

Approximate Controllability