# Controllability of the Strongly Damped Wave Equation with Impulses and Delay

Nonautonomous Dynamical Systems (2017)

- Volume: 4, Issue: 1, page 31-39
- ISSN: 2353-0626

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topHugo Leiva. "Controllability of the Strongly Damped Wave Equation with Impulses and Delay." Nonautonomous Dynamical Systems 4.1 (2017): 31-39. <http://eudml.org/doc/288492>.

@article{HugoLeiva2017,

abstract = {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.},

author = {Hugo Leiva},

journal = {Nonautonomous Dynamical Systems},

keywords = {semilinear strongly damped wave equation; impulses and delay; approximate controllability; strongly continuous semigroups},

language = {eng},

number = {1},

pages = {31-39},

title = {Controllability of the Strongly Damped Wave Equation with Impulses and Delay},

url = {http://eudml.org/doc/288492},

volume = {4},

year = {2017},

}

TY - JOUR

AU - Hugo Leiva

TI - Controllability of the Strongly Damped Wave Equation with Impulses and Delay

JO - Nonautonomous Dynamical Systems

PY - 2017

VL - 4

IS - 1

SP - 31

EP - 39

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/288492

ER -

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