Abstract
This paper considers the approximate controllability for a class of semilinear delay control systems described by a semigroup formulation with boundary control. Sufficient conditions for approximate controllability are established provided the approximate controllability of corresponding linear systems.
Highlights
For any y ∈ C −Δ, b ; E and t ∈ I, yt ∈ C is defined by yt θ y t θ for θ ∈ −Δ, 0
The state space E is a space of functions on some domain Ω of the Euclidean space Rn, σ is a partial differential operator on Ω, and τ is a partial differential operator acting on the boundary Γ of Ω
The purpose of this paper is to study the approximate controllability for a class of semilinear delay systems with boundary control
Summary
We consider the boundary control system described by the following delay differential equation:. We use the setting developed in 2 to discuss the approximate controllability of system 1.1. H3 There exists a linear continuous operator B : U → E and a positive constant K such that σB ∈ L U, E , τ Bu B1u, ∀u ∈ U, 1.3. Only a few papers dealt with approximate boundary controllability for semilinear control systems, in particular, semilinear delay control systems; the main difficulty is encountered in the construction of suitable integral equation to apply for different versions of fixed-point theorem. The purpose of this paper is to study the approximate controllability for a class of semilinear delay systems with boundary control
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