Approximate controllability of semilinear impulsive strongly damped wave equation

Hanzel Larez; Hugo Leiva; Jorge Rebaza; Addison Ríos

doi:10.1515/jaa-2015-0005

Published by De Gruyter May 13, 2015

Approximate controllability of semilinear impulsive strongly damped wave equation

Hanzel Larez , Hugo Leiva , Jorge Rebaza and Addison Ríos

From the journal Journal of Applied Analysis

https://doi.org/10.1515/jaa-2015-0005

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Abstract

Rothe'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 Z1/2=D((-Δ)1/2)×L2(Ω), where Ω is a bounded domain in ℝⁿ (n ≥ 1). Under some conditions we prove the following statement: For all open nonempty subsets ω of Ω the system is approximately controllable on [0,τ]. Moreover, we exhibit a sequence of controls steering the nonlinear system from an initial state z₀ to a neighborhood of the final state z₁ at time τ>0.