Controllability of the Strongly Damped Wave Equation with Impulses and Delay

• Autorzy: Hugo Leiva
• Języki publikacji: EN

Abstrakty

EN

Evading fixed point theorems we prove the interior approximate controllability of the following semilinear strongly damped wave equation with impulses and delay [...] in the space Z1/2 = D((−Δ)1/2)×L2(Ω),where r > 0 is the delay, Γ = (0, τ)×Ω, ∂Γ = (0, τ) × ∂Ω, Γr = [−r, 0] × Ω, (ϕ,ψ) ∈ C([−r, 0]; Z1/2), k = 1, 2, . . . , p, Ω is a bounded domain in ℝℕ(ℕ ≥ 1), ω is an open nonempty subset of , 1 ω denotes the characteristic function of the set ω, the distributed control u ∈ L2(0, τ; U), with U = L2(Ω),η,γ, are positive numbers and f , Ik ∈ C([0, τ] × ℝ × ℝ; ℝ), k = 1, 2, 3, . . . , p. Under some conditions we prove the following statement: For all open nonempty subsets Ω of the system is approximately controllable on [0,τ]. Moreover, we exhibit a sequence of controls steering the nonlinear system from an initial state (ϕ (0), ψ(0)) to an ε-neighborhood of the final state z1 at time τ > 0.

Słowa kluczowe

EN

semilinear strongly damped wave equation; impulses and delay; approximate controllability; strongly continuous semigroups

Kategorie tematyczne

• 93C10: Nonlinear systems
• 93B05: Controllability

• Wydawca: De Gruyter Open
• Czasopismo: Nonautonomous Dynamical Systems
• Rocznik: 2017
• Tom: 4
• Numer: 1
• Strony: 31-39

Daty

wydano

2017-04-25

otrzymano

2016-02-23

zaakceptowano

2017-05-02

online

2017-06-30

Twórcy

autor

Hugo Leiva

• ,

Identyfikatory

DOI

10.1515/msds-2017-0004