Controllability of the Strongly Damped Wave Equation with Impulses and Delay

Hugo 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 -