scholarly journals On the strongly damped wave equation and the heat equation with mixed boundary conditions

2000 ◽  
Vol 5 (3) ◽  
pp. 175-189
Author(s):  
Aloisio F. Neves
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Heat Equation ◽  
Mixed Boundary ◽  
Strong Solutions ◽  
Mixed Boundary Conditions ◽  
Global Attractors ◽  
Damped Wave Equation ◽  
Strongly Damped Wave Equation ◽  
Strongly Damped

We study two one-dimensional equations: the strongly damped wave equation and the heat equation, both with mixed boundary conditions. We prove the existence of global strong solutions and the existence of compact global attractors for these equations in two different spaces.

Approximate controllability of semilinear impulsive strongly damped wave equation

2015 ◽  
Vol 21 (1) ◽  
Author(s):  
Hanzel Larez ◽  
Hugo Leiva ◽  
Jorge Rebaza ◽  
Addison Ríos
Keyword(s):  
Fixed Point ◽  
Wave Equation ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Approximate Controllability ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Damped Wave Equation ◽  
Strongly Damped Wave Equation ◽  
Strongly Damped

AbstractRothe's fixed-point theorem is applied to prove the interior approximate controllability of a semilinear impulsive strongly damped wave equation with Dirichlet boundary conditions in the space

scholarly journals Controllability of the Strongly Damped Wave Equation with Impulses and Delay

2017 ◽  
Vol 4 (1) ◽  
pp. 31-39
Author(s):  
Hugo Leiva
Keyword(s):  
Wave Equation ◽  
Distributed Control ◽  
Fixed Point Theorems ◽  
Nonempty Subset ◽  
Damped Wave Equation ◽  
Initial State ◽  
Final State ◽  
Strongly Damped Wave Equation ◽  
Approximately Controllable ◽  
Strongly Damped

AbstractEvading 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.

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